I've found that much of the game's UX is not very intuitive, so in case you didn't find it you can access difficulty settings (including the Hard preset) by starting a Custom Game.

I currently favor the following roles for my four agents:

This agent spends almost all of their time hacking.

Requirements:

• 8 Intelligence
  
• Hacker trait

Nice to haves:

• Methodical (?)*
  
• Anonymous

*Many of the game's mechanics seem to not be fully understood, so I don't know if Methodical actually affects hacking and counter-espionage actions or not.

8 Int + Hacker seems to be needed to reliably reveal details of individual scientists when choosing hacking to locate scientists. It also makes reducing alarm by 30% fairly reliable.

This agent's priority tasks for most of the game are:

• Hack (from your home country) to find scientists in priority countries.
  
• Support current operations in a country by lowering alarm.
  
• In late-game, stealing/sabotaging the research of countries that are making progress on the final project.

Occasionally this agent may be needed to investigate enemy spies. Once in a blue moon they may also be needed to counter enemy spy activity when nobody else is available, since their high intelligence makes this viable in a pinch.

I currently like Aiekillu for this role. His negative traits don't matter if he never leaves the base, and he doesn't take up an elite slot.

This agent switches between hacking to lower alarm levels to support ongoing or expected ground operations in other countries, and finding and capturing enemy spies.

Requirements:

• 6+ Intelligence with Hacker trait, or 8 Intelligence without
  
• 6+ Strength

Nice to haves:

• Methodical (?)*
  
• Anonymous
  
• Hacker trait (strongly preferred)
  
• >6 Intelligence
  
• >6 Strength
  
• Traits which make finding and capturing enemy agents easier (e.g. Knife Fighter, Spy Hunter)

*Many of the game's mechanics seem to not be fully understood, so I don't know if Methodical actually affects hacking and counter-espionage actions or not.

This agent ends up being a strong all-rounder, able to catch all the work which the more specialist agents can't handle. They must have high enough intelligence to do medium-difficulty hacks reliably (e.g. lower alarm by >=20%) and find enemy agents, but enough strength to capture (not just counter) them once found. I find that any less than 6 strength + relevant trait will make them not reliable enough at captures, but you might be able to squeak by with a 4-5 if you have two relevant traits.

This combination of int and strength also means they can be pushed into the field opportunistically if needed, such as if one field agent gets captured and the other isn't able (for whatever reason) to bail them out, or if you just need to do any type of field work IMMEDIATELY at a time when other field agents won't be available for another turn (e.g. exfil scientists from a country that just dropped out, at a time when you have no priority hacking / counter-espionage needed).

Unless this agent has 8 Intelligence + Hacker, they should not be used to locate scientists in priority countries -- that should be left to your primary hacker instead. However, if you do choose an 8 Intelligence + Hacker agent for this role, feel free to use them interchangeably for hacking operations with your primary hacker.

I currently like Domingo for this role. Trojan is sometimes recommended by other players to fulfill a role similar to this (with the idea of more field deployment), though her mediocre strength will make capturing enemy agents less reliable (and thus you may need to compromise with countering rather than capturing, or possibly having one of your field agents perform some extra counter-espionage duties). I personally prefer to compromise slightly on hacking ability rather than counter-espionage, as your primary hacker can already be tasked with doing all of the most important hacks, and strong (rather than adequate) counter-espionage currently seems like a preferable compromise to me.

I also see some players recommend Red Sword for a similar role to what I've described, but I feel like the tradeoff for having an elite in this role isn't worth losing an elite for my strong field agent.

Deploying agents to the field (and bringing them back) takes time, so I feel like it's better to avoid the downtime inherent with traveling to other countries when possible, and to instead keep your secondary hacker at home where they can have maximum uptime.

This agent needs to be able to reliably turn enemy scientists, but also be able to exfil them even if the country's alarm level is high.

Requirements:

• 6+ Intelligence without many negative scientist-turning traits, 8 Intelligence with
  
• 6+ Strength

Nice to haves:

• 8 Intelligence (strongly preferred)
  
• >6 Strength
  
• Different gender to secondary field agent (to improve seduction coverage)
  
• Master of Disguise trait
  
• Traits which make turning enemy scientists easier (e.g. Seducer, Puppet Master)
  
• Traits which make exfil much more reliable (e.g., Blackbelt, Exfiltration Expert)
  
• Traits which make exfil slightly more reliable (e.g., Wheelman, Negotiator)

Notable negatives:

• Loner
  
• High Profile
  
• Stubborn, unless 8 Strength or 6+ Strength but with strong exfil traits (during difficult exfils, getting a bad outcome on any of the checks can be very dangerous!)

This agent is usually my elite. They basically have to be able to go into hell and come back with a scientist if need be. High intelligence is needed to not only make turning scientists more reliable, but to make it faster, and this is why I currently prefer using an 8 intelligence agent for this role, even if it means compromising in some other areas.

I strongly prefer if this agent has either 8 strength or 6 strength but strong exfil perks (e.g., Blackbelt), so that they can reliably make it out of even tough exfiltration jobs without a couple of bad dice rolls leading to their capture.

I currently like Wolf for this role. Although his Honest and Weak-willed traits pull his effective intelligence on scientist-turning-reliability down to something like 6 (I'm estimating, I wish we had the exact numbers!), what these negative traits don't seem to do is reduce the time savings. In my experience, Wolf can typically perform ~1.5 seduces / bribes / conversions in the time it would take a 6-int agent to do 1, and this faster speed seems to result in a net gain in total conversions, despite his lower success rate.

8 Intelligence also means he can reliably pull off fast investigations if that's ever needed (e.g. for counter-espionage if you're being riddled with spies, or in other countries if your primary hacker fumbles while locating scientists).

8 Strength allows him to knock out 4 police at a time during exfils (without resorting to killing anyone). Having 8 of both stats means that he will usually succeed in all strength and intelligence checks during exfil (which is most of them). This allows him to take on difficult exfil missions (high initial alarm level) and reliably succeed.

I've experimented with Espoir and Scarfor this role and have also seen some players recommend Red Sword or Morrigh4n for a role similar to this, though for the reasons I've discussed I still currently prefer Wolf.

This agent needs to be moderately good at turning enemy scientists (though better is better!), but only needs to be able to handle the easier exfils because you'll have enough hacking power to get alarm level down for them.

Requirements:

• 6+ Intelligence without many negative scientist-turning traits, 8 Intelligence with
  
• 3+ Strength

Nice to haves:

• >6 Intelligence
  
• >3 Strength (ideally 5+ to be able to improve reliability in medium-difficulty exfils)
  
• Different gender to primary field agent (to improve seduction coverage)
  
• Master of Disguise trait
  
• Traits which make turning enemy scientists easier (e.g. Seducer, Puppet Master)
  
• Traits which make exfil much more reliable (e.g., Blackbelt, Exfiltration Expert)
  
• Traits which make exfil slightly more reliable (e.g., Wheelman, Negotiator)

Notable negatives:

• Loner
  
• High Profile
  
• Stubborn, unless 6 Strength or 6+ Strength but with strong exfil traits
  
• Too many traits which make turning scientists more difficult, unless compensated with intelligence or positive traits

If your strong field agent is an elite male (Wolf), there are very few choices that give you the female complimentary synergy that you want to improve seduction coverage and handle scientists who are either wary of men or wary of women.

When using Wolf, I currently like Zenith for this role. She's nothing special, but 6 intelligence + Negotiator is adequate (though not great) for turning scientists, while 3 strength + negotiator + wheelman is enough to get through the easier exfil missions. There are many alternative agents that can do an adequate job in this role, especially if you end up choosing a female agent for your "strong" agent. Remember that if you choose someone with some negative traits like Arrogant this will hurt their reliability -- and reliability is very important if the agent doesn't have enough strength / traits to handle an exfil that goes south.

I've experimented with using Saint and a few other agents in this role, but currently prefer the strong Wolf + weak Zenith combination.

I've previously focused this role more on having stronger exfil (e.g. using Catch), but I believe this approach is worse than focusing more on turning scientists and then using hacking to make the exfil easier instead.

Other countries will research at 3x your speed, so if you don't simultaneously get yourself ahead-of-default and get others behind-of-default, you'll end up being knocked out for being last in research.

Thus, my preferred strategy during the early game is to focus on exfiltrating scientists from one country at a time. This involves initially getting your strong hacker to hack-locate scientists and your weak hacker to get the alarm down. You may then followup with whichever hacker is available to keep the alarm low enough to reliably succeed in your exfils (remember a weaker exfil agent like Zenith will probably need alarms down to 0-20% if you don't want to risk bad RNG causing the exfil to fail).

Russia seems like a good first target, because one of their two scientists is going to be a genius.

Some things I suggest avoiding:

• Spreading out your efforts to two countries simultaneously too early into the game will give them each a chance to use one scientist to outpace your 2-3 scientists (which increases the risk of being in last when a country gets culled).
  
• Focusing early hacking on stealing/sabotaging research progress. Stealing scientists is far better, as it simultaneously reduces all future research progress in that country whilst increasing yours. Stealing/sabotaging is only a once-off, and it looks like it will only either reduce their research or increase yours, not both.
  
• Don't get your field agents to do exfils beyond their capabilities. Wolf at full health can usually get through even a 100% alarm, but it's less risky if the alarm is only 60-80% in case you get bad RNG on the exfil. If feasible, a medium-capability exfil agent should only doing up to 50-60% alarm, and a weak exfil agent should only be doing up to 20-30% alarm. If one of your agents gets captured in the early-mid game, your chance of losing increases substantially, ergo: set your agents up for success on their exfils, not failure.

I like to focus early diplomacy on shoring up the countries with the weakest (and thus most at risk of blowing up the doom clock in the event of e.g., hacking failures) by giving out research. Since everyone researches at 3x your speed, your early research goal is not to be in the lead, it's to avoid being at the bottom when the culling happens. Trading research early gives away very little (because your third-speed scientists will have made almost no progress) but is quite reliable for improving relations.

Once you've taken the first country's scientists, move onto the next country. You should be able to reliably get at least 3 scientists from two countries in the early game, which should give you enough research progress for your (5 * 33% = effectively 1.66) scientists to beat whichever poor countries end up on only 0-1 scientists, whether by your actions or the actions of other countries.

Support your exfils with the recon drone once you have it, and start using your combat drone to boost relations by sending it to support the military operations of other countries. You can also optionally send it to support exfils, but I personally try to maintain a no-deaths policy as much as I can.

Remember that you want scientists to be identified (by an 8 int + Hacker trait hacker) in a country by the time your field agents land so that they can immediately get to work on turning them. This isn't possible for the first country, but should be the goal for subsequent countries when possible.

I generally suggest focusing your exfil efforts on the strongest countries (with the most research progress). You should be able to steal scientists just fast enough to outpace whoever's at the bottom of the leaderboard without needing to explicitly focus them, and this has the benefit of both slowing down the mid-game.

You will usually have to cooperate with the terrorist organizations early on, as e.g., losing a scientist early is too costly. If you want to turn on them (or just ignore them), you'll probably have to wait until mid game to do so -- and you probably should choose that rather than full cooperation since that's better for the doom clock.

You probably can't afford to help your spouse early on, as getting past the early game is the hardest part of Hard mode. If you want to play nice with them, it'll have to wait until mid game when you're in a decent position.

I generally suggest focusing your exfil efforts on the strongest countries (ones with the most research progress). You should be able to steal scientists just fast enough to outpace whoever's at the bottom of the leaderboard without needing to explicitly focus them, and this also has the benefit of slowing down the transition from mid-game to late-game (when countries are on the final sigma tech).

Make counter-espionage a high priority in mid-game while continuing to empty other countries of their scientists. These captured Scientists are a significant investment, and losing them is costly for you. When multiple scientists are available, prioritize which scientists you take: for example, charlatans are obviously less valuable, but prisoners are also lower priority because although they're full value to you once exfil'd, they're less than full value to the country where they currently are -- so leaving them until last along with the charlatans hurts their research more at no cost to you.

I personally find that both diplomacy and interrogations are not super important most of the time other than avoiding hitting 0 to keep the doom clock in good shape, but they'll give you a small boost if you remember to do them.

For diplomacy, you can trade away economic favor to improve relations since the resource it costs (relations with your own country's government) is easy to replenish due to successful exfils. Captured agents can be used to gain research or even enemy scientists, but remember to try interrogating them first. Avoid killing agents during interrogations!

Avoid actions that significantly increase the doom clock, such as the +10 hit you'll take for giving away certain research to the private orgs.

If a country seems to get into a breakaway lead, you should re-focus on stealing their scientists. Better to leave your existing target half-finished than to have a country end up researching the final project way before you're ready to handle that.

While you may or may not be the first to reach the final project, once either you or multiple countries are researching it (and actually making progress), I'd consider mid-game over.

By this point there will only be a few nations with enough scientists to compete for the final tech, as you'll have stolen most of the world's scientists for yourself.

You'll need to start balancing your hacking efforts between sabotaging the current research leader(s) and stealing their scientists. It may even be worth periodically getting one of your returning-from-exfil field agents to stick around for a couple of turns helping with counter-espionage to free up more hacking time.

Remember to continue using diplomacy and interrogation for a small edge if you need it and can be bothered.

If you reach this point of the game successfully, the game should essentially be over, as you'll only need to compete against at most around 3 other countries, and this is easy to do with hack + hack + steal scientists for each of the three respectively.

• It may be worth getting BOTH hackers to look for scientists at your target destination on the first turn, as even an 8 int hacker with the Hacker trait will sometimes fail to find the scientists' weaknesses. This especially true if you have someone with amazing exfil (e.g., Wolf), as the chances of them failing an early exfil without alarm-hacking support is low. Since I don't have the game's raw probabilities to calculate with, it's hard to come to a firm conclusion with limited sample size.
  
• In the short term it's more important to mitigate the last-place-in-research loss condition if a loss appears imminent (e.g., due to bad luck) than it is to focus on long-term success (via scientist-stealing). For example if the last-place-culling has yet to occur, two or three nations have completed new research, and you're still stuck at the bottom, your overall win rate will probably be higher if you temporarily focus on hacking the ♥♥♥♥ out of one of the bottom-ranked nations (ideally one you think has few/no scientists) to steal and sabotage their progress enough for them to be pushed to the bottom.

With the right setup and strategies, I think you can probably win half or more of games on Hard -- I haven't played enough to get a large sample size, so can't give a more specific estimate such as "two thirds". Once your strategy is optimized and your execution is solid, there still seems to be a lot of RNG involved about whether you can make it through to late game, so it seems like some losses must be expected.

These are the ideas that helped me to win on Hard -- hopefully they've helped you as well! Feel free to leave your own advice, but do make sure you can actually achieve success with whatever you recommend. Tips that you "thin should work" but which you've never won with are highly suspect!

There's also plenty of information scattered throughout the Steam forums and a couple of other guides, but I encourage you to figure out some your remaining questions on your own. The lesson you teach yourself is probably more insightful than the lesson learnt from someone else.