This guide is based on my own experience/research done while completing the game 100% myself, as well as information found online that I was able to confirm through testing. Some information in the guide might be based on speculation or incomplete (I was not able to test every combination of factors for every achievement). If you can prove that one of the claims I make here is incorrect or missing some important addition, please let me know in the comments.

Before getting into specific achievements, here is some general information that is worth keeping in mind while going for 100% completion - some of which the game does not convey very clearly, if at all. These tips don't pertain to any single achievement, but can be useful in getting all of them.

• The clutch mechanic is this game's "nitro", essentially. You will need it to do well in some of the more difficult races.
  
• Difficulty has no bearing on your ability to get achievements; this means that increasing the difficulty of the career, AI efficiency, vehicle damage, number of laps etc. has no related achievements and the fastest way to complete the game is to set everything to minimum at all times. Feel free to adjust the settings to your preferences without worrying about missing out on any trophies.
  
• Changing the "career difficulty" setting from "easy" to "hard" switches your handling from arcade to simulation mode and increases AI driving efficiency. Unfortunately, there is no way to separate the two settings. Keep in mind that while the career starts out really easy, the difficulty does increase with each class.
  
• AI opponents get a performance boost based on your car's upgrade level, but only in some modes.
  
• There is no way to remove upgrades from your car. The only way to do so is to sell the vehicle entirely.
  
• You can only sell cars that belong to a class you have at least one other vehicle in. If you only have one car in a certain class, you can't sell it.
  
• Quick (non-career) races let you use your career cars. These retain all of their upgrades, making them superior to all the sponsor-specific vehicles you will unlock as you win races in the career.
  
• Sponsors are assigned randomly - a new sponsor may offer you less money than your current one. Always pay attention to the payout comparison before switching sponsors. Also, sponsor money is very important - at the end of the career, they pay you more than winning the races does, provided that you can keep your car relatively intact. You will need these funds for some of the achievements.
  
• Class 1 unlimited buggies are comparable, if not superior, to trophy trucks - despite the trucks being the final class, they actually share the exact same top speed with the buggies (199 km/h for a fully upgraded car) and any advantages they have are offset by their terrible weight distribution and inferior handling, which makes them prone to tipping over and makes it more difficult to maintain high speeds. Before you start using trophy trucks for non-career events, make sure you're not more comfortable with class 1 unlimited buggies. The game treats them as equal, as long as you select "competitive classes" in the AI class limit setting.
  
• Most rally races are similar in length (about 15 minutes with arcade controls and no damage). There are a few exceptions, however, the most noteworthy being Sky Ranch Rally (~3x shorter) and Jade Reef Rally (~5x shorter).
  
• The shortest circuit race, as far as I can tell, appears to be Beetle Spring of the Uyuni Salt Flats environment.
  
• Since the game doesn't really explain the damage system outside of some loading screen tips (which you probably won't have time to read), here is a breakdown of what the gauges actually mean:
  - H2O: this is your water temperature (that's why it goes from 0 to 100, not the other way around like everything else). It is affected by the environment - on some tracks, it won't go down past a certain level. If you overheat, your car slows down. You can cool down by simply letting go of the accelerator (on some tracks, even a second of downtime lets your engine cool down significantly). Even though this is technically not a damage indicator, repairing your car in a hot pit (or at a supply chopper) brings this gauge back to minimum level much faster than waiting for it to go down naturally.
  - Oil: goes down as you use the engine. Letting go of the accelerator stops its consumption. When it goes into the red, your car begins to slow down. Once it's depleted, you'll be moving very slowly. This is usually the gauge that will go down first and your choice whether to repair will be based on it most of the time.
  - Tires/brake: practically meaningless. Tires wear down naturally over time (decreasing traction), brakes wear down as you, well, brake (decreasing their stopping power). However, these gauges tend to go down so slowly (as long as you upgrade your car) that something else will always force you into the hot pit before they can become an issue.
  However, tires can burst regardless of their condition. This is caused by rough landings - whenever you land without all four of your wheels touching the ground, the ones that land first can burst. Flat tires affect your steering, but also slow you down. Every car carries a spare tire (or two), which can be used to replace a flat by coming to a complete stop and pressing the repair button. A hot pit (or supply chopper) will replace all your flats and replenish all spares. Spare tires can also be lost if they come loose in collisions.
  - Shocks: they wear down during rough landings. Use the airborne controls to keep your car parallel to the ground when landing in order to minimise this. Once the gauge goes into the red, your car begins wobbling uncontrollably.
  - Clutch: wears down as you use the clutch, obviously. However, like the tires and brakes, it gets damaged so slowly that you might as well ignore it altogether. Presumably, it decreases the efficiency of your clutch boost, but I never even had a chance to test it.
  
• You do not need to be at a complete standstill to repair your car at a hot pit or supply chopper. This means that you can start moving before the gauges are completely refilled - you'll still get at least 10-20% in each of them as you start to accelerate.
  
• The AI can call in the supply chopper, but this is very unreliable. Often, the chopper won't land at all and will just keep switching landing spots on the minimap. If you need repairs, call it yourself. Sometimes, it will refuse to land - keep trying until it changes its mind. And do not pass the chopper - it will fly away almost immediately.
  
• The reset mechanic is very easy to abuse. You can reset any time you want, which puts you back on the track, facing the right direction, and gives you a period of no collision with other cars. This lets you easily avoid the results of crashes, instantly regain control when you spin out or go off track (or even before that - there's nothing stopping you from using it pre-emptively to avoid a crash). The only downside is that you start from a complete standstill. And don't use the reset on bridges - you may spawn below or inside them (if this happens, keep resetting until the game remembers how physics work).
  
• The best way to drive is to perform lots of small jumps. Let go of the accelerator in mid-air (so that your temperature and oil consumption are lower), then, as you land, rev the engine back up using the clutch and let go of the clutch once on the ground, making you go even faster. Learn this rhythm and you'll be reaching your top speed faster while having to repair your car less.
  
• Some of the hardest achievements in the game are ones that require you to win every single race within each environment. This is hard because the game does not keep track of which races you've already won. This will be discussed further in the appropriate section of this guide, but the safest way to deal with this is to make notes yourself. Otherwise, you may find yourself having to redo a bunch of races for no reason.

With this advice out of the way, here is the breakdown of all the achievements (including some more specific tips related to each of them):

Watch all of the tutorial videos.
The tutorial videos can be viewed in the quick race menu - select a type of race for the first time and the appropriate tutorial video will play automatically. You can replay it later with a button prompt within that race type's sub-menu. Watch the videos for each race type (including Free Ride) and the achievement will be unlocked.

Finished a race in first place.
This achievement seems to refer specifically to a quick race; there is a separate one for winning your first career race. Other than that, any race type can be used for this.

Won three races in a row.
You need to get 1st place in three races of any kind in a row. This can be done in the campaign.

Completed an entire race without ever leaving the track.
"Leaving the track" means having the "Get back on the track" warning appear for even a split second. The exact confines of the track can be somewhat unclear on some courses, so I'd recommend doing this on one of the shorter ones (like Beetle Spring). Also note that the condition is "completed", not "won". Can be done in any mode.

Finished a race without any body panels attached to a vehicle.
This can only be done if vehicle damage is set to either "full" or "cosmetic only". In the career, the former option is always on. All you need to do is keep crashing until there are no panels left on your car - I recommend using some type of buggy, since it's very clear which panels can be detached from the frame in their case. Afterwards, you only need to finish the race in any position. Can be done in any mode except Free Ride - Free Ride can't be "finished".

Finished a race in 1st, 2nd or 3rd with no body damage what so ever [sic].
"No body damage" means that all of the panels (and other bits - you can also lose spare tires and some other small parts) are still on your car. It's still OK to touch other cars/obstacles, as long as nothing falls off. Keep in mind that the damage model is pretty random, so it's better to stay away from the opponents anyway. Can be done in any mode, including the career.
Or you can just cheese it - setting vehicle damage to "off" in a quick race means you automatically finish it intact. I haven't had the chance to test this myself, but it works with the next achievement, so I assume it does with this one as well.

Finish a race in 1st, 2nd or 3rd with no flat tires.
Tires burst primarily on rough landings, as described in the general tips section. To avoid it, land on all four wheels using the aerial controls.
Or cheese it - setting vehicle damage to "off" or "cosmetic only" in a quick race disables tire popping completely and you will still get the achievement with those settings.

Get fully repaired in the Hot Pit for the first time.
"Fully repaired" means that all your gauges are back to full. It doesn't matter how low they were when you arrived at the pit. Simply stop in the hot pit (the grey rectangle with a big truck next to it) and wait until the repairs are complete. Can be done in any Circuit Race or Open Class Challenge (career or otherwise) as long as full vehicle damage is enabled (otherwise your gauges won't go down).

Get fully repaired by the helicopter for the first time.
"Fully repaired" means that all your gauges are back to full. It doesn't matter how low they were when you arrived at the helicopter. To summon the supply chopper, press the repair button - a blue square with an "H" on it will appear down the road on the minimap. Once the helicopter (represented by a green circle on the minimap) arrives there, it will land and you will be able to stop by it to get repaired the same way you would in a hot pit. Sometimes, the chopper will refuse to land - keep pressing the repair button until it changes its mind. Can be done in any Rally (career or otherwise) or Baja as long as full vehicle damage is enabled (otherwise your gauges won't go down).

Roll your vehicle at least 3 times in a row.
The physics in this game are somewhat fanciful. It appears that when you crash in certain ways, your car enters a different "mode", in which it is far more likely to flip/roll. You can recognise this by the camera zooming out and no longer following your vehicle the usual way. The easiest way to get this achievement is to land on your side/front/rear when jumping off a mountain - it can be done in any mode, but you'll get the most opportunities to do so in Free Ride. You don't need to finish the race afterwards.

Achieve a minimum top speed of 120 MPH.
Despite the awkward wording of the achievement's description, it just wants you to reach a speed of 120 MPH. This is around 193 KPH, so actually really close to the highest speed you can achieve in the game (199 KPH). You'll definitely want to use a class 1 unlimited buggy or trophy truck for this, though it doesn't need to be fully upgraded if you find a good downhill stretch of road. The easiest place to do this achievement with a sufficiently fast car is on a highway - many rallies feature stretches of straight(ish) tarmac roads, though you should also be able to do this in Free Ride mode.

Accumulate a total of 1 mile of distance traveled while airborne.
Self-explanatory. You'll most likely get this achievement after just a few short races.

Use the hand brake at least 5 times in one race.
Not quite as obvious as it might seem. The achievement doesn't appear to simply be counting how many times you push your handbrake button - instead, I believe it counts how many times you manage to perform a drift while using the handbrake. Hold down the handbrake while entering tight corners and hope it counts. You'll know once you've succeeded, as the achievement pops up immediately after the 5th "handbrake use".

Use the clutch at least 5 times in one race.
This achievement seems to count how many successful clutch boosts you've performed in a race. To do a clutch boost, hold down your clutch button for a moment, then let go. This causes you to slow down for the duration of the clutch being held down, but then get a noticeable speed boost once it's released. This is best used in mid-air, when drifting, or from a standstill in order to negate the slowdown. It's important to master this technique if you want to do well in races. You'll know once you've succeeded, as the achievement pops up immediately after the 5th "clutch use".

Use preload at least 5 times in one race.
A "preload" is a weird trick you can do in this game using the aerial controls. When approaching the crest of a hill (or even a small bump, really), lean your car forward, then switch to leaning back once you reach the top. This will cause your car to suddenly pop up into the air. Note that there seems to be no indication that you're doing it right until you pull back and the car gets flicked up. It's not particularly useful in practice, but you need to learn it for this achievement. You'll know once you've succeeded, as the achievement pops up immediately after the 5th preload.

Finish 1st in a race with the AI and Laps set to 5 or more using a manual transmission.
In order to change your transmission type, go to the settings menu and select it in the "driving physics" tab, in the "player 1" section. You'll need to do any race (career or otherwise) with it set to manual. If you're not good with manual transmissions, you can simply do a quick race, lobotomise the AI and use a fully upgraded career car to give yourself every possible advantage. Keep in mind that it has to be a Circuit Race and you do need to set the number of laps and AI cars to at least 5. As recommended before, Beetle Spring is most likely the shortest circuit in the game.

Finished a career race in 1st place.
Self-explanatory. For reasons explained later on, I highly recommend that you finish every career race in 1st place.

Finish in 1st place in any league during your career.
Self-explanatory. While you don't need to be 1st in every single race in order to be 1st in the whole league (assuming the same AI driver doesn't end up beating you in most races), I still recommend that you do so for achievement hunting purposes.

Earn enough experience points to unlock the [class name] race leagues.
These are all simple - just keep winning races to get experience points and eventually, you'll unlock every class. You don't need to win/complete all leagues within a class to unlock the next one, but you still need it for other achievements.

Finished 1st in 5 Invitationals races.
The achievement itself is fairly self-explanatory, but there are some major things of note here:
- Invitationals are unlocked in the career as you complete races. You access them from a separate section within the career menu (which doesn't appear if you have no invitationals available at the moment). Each invitational has a date on which it happens - you can only access it if the current date matches. The current date is displayed in the career menu; it starts out as January 1st, 2017, and progresses as you participate in races (or win them - I wasn't able to confirm which it is).
- Invitationals do not count towards career completion! Your career stats screen shows a completion percentage for invitationals, but this is irrelevant. You don't need them for the "Career complete!" achievement. They're just a way to earn some extra money.
- While you need to do invitationals for this achievement, they actually make it more difficult to track your progress for other achievements. For the sake of those other achievements, I would recommend sticking to Circuit Race invitationals; however, Rally invitationals seem far more common and it may be somewhat difficult to find 5 Circuit Race ones during a single career. If you decide to do the Rally ones, write down which Rally tracks they featured or make sure you win every one of them.

Completed 100% of the career!
For this, you need to get 1st place in every league/event. By events, I mean the career Rallies and Open Class Challenges. In leagues, you don't need to win every single race, just place 1st at the end. You can view your completion percentage for each class in the career stats screen, so it's easy to keep track of what you need to complete/redo if you miss something.

Have 1 million credits in your account.
To unlock this, you need to have at least 1 million credits in your account at the same time - any credits you've already spent don't count (although you can sell cars to get them back). However, this achievement seems to be somewhat bugged and it doesn't unlock immediately. Continue playing and it should eventually unlock, but to be safe, I'd recommend not going below 1 million credits until it's unlocked.

In terms of strategy, you will need this kind of money anyway to enter the trophy truck class; however, if you don't want to replay races, you'll actually find yourself with only just enough funds to buy and fully upgrade your cars in the last few classes. Remember to keep your car as intact as you can in each race to maximise your sponsor payouts, because you'll need that extra money. The best moment to go for this achievement is once you've already reached the trophy truck class, as victory and sponsor payouts increase substantially with each class. Completing the trophy truck class should easily get you more than enough money to get the achievement - just make sure to wait before you start spending it on extra cars for other achievements.

Purchased 15/25 vehicles.
While the descriptions are self-explanatory, it's worth noting that 15 vehicles is far more than you'll ever need. There's little to no advantage to owning more than 1 vehicle per class, and if you don't want to replay races, you'll need to save as much money as you can to enter new classes. Therefore, I highly recommend only going after these achievements once you already have a fully upgraded car in every class. Obviously, you'll want to start your purchasing spree with the lowest classes.

Potential cheese opportunity: I can't confirm this, but it appears to me that cars you buy and then sell still count towards the achievements. I would greatly appreciate it if someone could test this, because if it's true, it means you can just buy the same car 25 times and get both achievements.

Finished 1st in every race in [location name].
While winning the races (Circuit Races and Rallies, to be specific - both are required for these achievements) is not really a problem - you can do it in the career or in quick races - the issue is that you need to keep track of which races you've won, as the game doesn't do it for you. So, as mentioned before, the best way to deal with this is to write down the name of each track you win a race on. However, many players won't know to do this from the start, so here is some knowledge you might use to circumvent this to some degree:
- The options menu has a "track records" section. If you haven't ever raced on a track, all fields for all car classes for that track will be empty. The issue is that this only tells you if you've completed that track, and you need to win all of them. That's why I've repeatedly recommended that you get 1st place in every race you do - otherwise, it will become impossible to tell which tracks you need to redo.
- The career features every single Circuit Race. If you win every race in every league, you will have also checked off all Circuit Races. Most (if not all) races get repeated at least once, too.
- Open Class Challenges don't seem to count towards these achievements (which makes sense, as they have their own achievement and they reuse Circuit Race tracks anyway).
- Bajas are really just marathons of non-stop Rallies, but they don't count as winning the individual Rallies!
- Even though invitationals don't require you to win every single one of them for any achievement, participating in invitational Rallies and not winning can get you in major trouble. The career doesn't cover every Rally track, so you might end up setting a record on a track you haven't done before, which will make it impossible to tell that you haven't won that one from the track records. So either win all invitational Rallies you participate in or skip them altogether.
- Free Rides don't count towards these achievements in any way.

Finished 1st in every Hill Climb race.
Just complete the career and you will have done every Hill Climb along the way. Incidentally, these are some of the easiest races to win, as the AI can't really handle them.

Finished 1st in every Open Class race.
Two major things of note here:
- The career includes every Open Class Challenge except the Mogollon Rim one. Win every Open Class race in the career and do the Mogollon Rim one through a quick race.
- While these challenges start out easy, they get harder with each class; this will eventually become a serious problem, as the later ones are by far the most difficult races in the whole game. This is because, unlike in most modes, the AI scales its cars to match your upgrade level. This means that if your car is fully upgraded - which it should be for all other races - the AI becomes really hard to beat. The solution is to use a car with only the tires and the clutch upgraded. This way, you still have the maximum advantage of the clutch boost, but the AI cars can't use their upgraded engines against you. Since you can't downgrade your car, you may need to buy a disposable one just for this one event, or simply do this event before you upgrade your main vehicle. And no, this trick doesn't work in Rallies etc.

Finished a Baja 250/500/1000.
Self-explanatory, but remember to do the Baja 1000 with a trophy truck - otherwise you'll have to complete it more than once to get all achievements. Some minor things of note:
- Bajas are just collections of non-stop Rally tracks. If you're not going for 100% achievements and you only want to see everything this game has to offer, there is no Baja mode-exclusive content.
- These events are very long and you can't return to one after you've quit it. Make sure you are prepared for a longer session before attempting one.
- Despite being long, they're not quite as long as the game would have you believe. As stated before, you can complete most Rallies in 15 minutes or so with the right settings (the Bajas seem to avoid the unusually short Rally tracks). With this knowledge, you can easily calculate how long each Baja will take - and the times suggested by the devs are rather generous.

Complete the Baja 1000 in a Trophy Truck.
Self-explanatory. You need to do the Baja 1000 for a different achievement, so remember to combine the two.

Fun fact: the icon for this achievement shows a full-size truck, not a trophy truck. Oops!

Found every hidden Discovery in Free Ride.
The rarest achievement in the game. Within every Free Ride environment (which is really just the map used for all the tracks within a given environment), there are 5 arbitrarily chosen "landmarks" you have to discover. The issue is that some of them are hardly landmarks at all and some have very specific requirements as to where you need to be exactly for the "discovery" to count. The options menu tracks your discoveries in each environment, but only their number - so I'd recommend doing them in one sitting, lest you forget which landmarks you've already visited. Discoveries do work in multiplayer, too.

If you want to do this on your own, it will most likely be very tedious; thankfully, some kind soul has already made a video guide for this achievement before. While it may not be much fun to follow it blindly, it's by far the most efficient way to check off this annoying achievement:

Drove 1000/2000 miles in all vehicles combined.
A simple couple of achievements in concept: all you need to do is drive for 1000 or 2000 miles, respectively. This counts your distance travelled in real time, so it does count progress within events you quit instead of finishing - meaning your progress is also counted in Free Rides. However, as far as I can tell, multiplayer doesn't count! I don't know why, but doing a Rally fillled with AI cars in multiplayer didn't give me any progress towards these achievements, so I would definitely recommend against trying to complete them online. Two more things of note:
- Even though these achievements have progress bars, they aren't updated in real time. You need to quit the game before your progress appears on the bar. This is not true for milestones - those will still pop up in-game. As will the achievements themselves, so don't worry - you'll know as soon as you've reached the necessary distance travelled.
- The first achievement will be unlocked organically if you're trying to complete the game 100% - there is no way you can do all the other achievements without travelling 1000 miles. However, this is not the case for the second one; you will need to farm extra miles if you've been efficient with everything else. In fact, I ended up needing to do multiple extra Rallies, Bajas etc. The only way to cheese it I can think of is to start a race and lock your accelerator in some way so that your car continuously goes off track, gets reset, rinse and repeat. This will still take a while, though.

Play at least 5 hours in Multiplayer.
Self-explanatory, but not necessarily easy, given there aren't exactly lots of online players for this game these days. If you're trying to cheese this achievement for 100% completion, the best way to do it without having to do an extra 5 hours of grinding is to select a short online Circuit Race set to 2 laps, then leave it running for 5 hours (you can do this in several shorter sessions too, of course). Remember that you need to complete the race afterwards and that only the time after the race begins counts! The timer for this achievement doesn't start until you select "start race" from the menu and wait the extra minute. This also means no Free Rides. Do not pause the game! When you do that, your car starts to drive on its own. Not only will this complete the race, the time spent online with the pause menu open does not count towards this achievement. It doesn't count towards the "Mille Bournes" achievements, either.