I've assembled these steps and summary from my playthrough experience, a few guides/comments here in Steam Community and some Reddit posts. Hurts too see so many clickbait pages have copy-pasted this (some of them including the very title letter-by-letter) within hours/days without even giving the slightest credit. When in doubt, check the creation dates :)

Update 23.12.2022: Thanks to HamAndSomeCoffee on Reddit, I've updated the guide for Beyond Time and Space achievement. Turns out it relies on specific choices starting with Chapter 2 - Rockatansky D79.

Update 23.12.2022: Tip for a possible way of obtaining What They Hide From Us in the WIP section, thanks to Natjur mainly.

- Fail to make it past the prologue

Description: Disable your Mess Hall, set the game to maximum speed and wait till you fail. (Update: Build it first, apparently the game doesn't trigger starvation before your first ever Mess Hall.)

- Discover Outer Hope during the prologue

Description: Send a probe to almost directly East (very slightly South) of Moon to discover Unauthorized Access location and complete the events. (Just visiting might be enough, but the rewards are quite worth 30 Alloy during early game anyway.)

- Implement the Naomi protocol 3 times

Description: While you are at the achievement above, choose the Naomi option to make it count towards the achievement. ("Naomi Protocol: Create a temporary easement")

- Use the body of Oulixes to access the Thianki

Description:
- Do not start the Neptune event before you find and complete the Saturn event.
- Saturn choice: Make contact > Break through the ice.
- Neptune choice: Use Oulixes' biometric data to open the sealed room

- Implement the Naomi protocol 3 times

Description:
- Discover Uranus with a probe.
- Start the science event.
- Choose the Naomi option. ("Naomi Protocol: Cut down the tree")

- Replace Edden with the P.A. of the Protagoras

Description:
- At the end of the Chapter 2 - Protagoras main quest event, choose "Naomi protocol: Save a copy of the Protagoras' P.A." option to be able to achieve this later.

- Implement the Naomi protocol 3 times

Description:
- While you are at the achievement above, choose the Naomi option to make it count towards the achievement. ("Naomi Protocol: Save a copy of the Protagoras' P.A.")
- During the main quest event Man is the Measure of all Things, choose the Naomi option.
-- At this point, your 3 times should be done, but some redundancies nevertheless:
-- Science Event Mack R: ("Thaw the Ice" -> "Naomi Protocol: Send a team")
-- Science Event Tatra v8: ("Naomi Protocol: Interrogate the P.A")

- Use exoskeletons to ensure no crew members die on Fargo 39

Description:
- Before starting the Fargo 39 science event, make sure you researched Exoskeletons upgrade in the Tech Lab under Science Ship.
- Choose the corresponding option during the event. ("Deploy the entire crew in reinforced exoskeletons.")

- Entertain your crew members

Description: This is not actually Chapter 2 specific, but probably the best time to do it here.
- Set up an Alternative Life Center as soon as you can and this one will pop up by itself eventually.

- Finish the chain of events concerning the strange spheres

Description: Science Event - Rockatansky D79
- Establishing infrastructure to support exploration and geological analysis.
- Descend to the cavity and study the sphere.

- Adopt the borzoi

Description: Visit Collapsed Food District and complete the events with these choices: Investigate the Animal Pens > Naomi Protocol.

- The borzoi survives the journey

Description:
- Shortly after you adopted the Dog, the P.A. will ask you whether to exterminate it for health purposes or keep it.
- Simply keep it and you will get the achievement when you finish the game.

- Implement the Naomi protocol 3 times

Description: While you are at the achievement above, choose the Naomi option to make it count towards the achievement. ("Naomi Protocol: Create a temporary easement")
- At this point, your 3 times should be done, but another redundancy nevertheless:
- Science Event Collapsed Food District: ("Investigate the animal pens > Naomi Protocol")

- Free ZY6073

Description:
- Discover Medical District Wreckage with a probe.
- Make a manual save, because your entire crew will be killed and you will retrieve only ZY6073 and your science ship.
- Start the science event.
- Choose Investigate the Research Facility -> Retrieve ZY6073.
- Get the achievement and load your save, then choose a safer option or leave.

- Finish the chain of events concerning the strange spheres

Description: Science Event - Cruc-P-43
- Use explosives to quickly clear a path.
- Examine the sphere.
- Study the concentric circles.
- Leave the planet.

- Have a member of Tiqqun compose a rap song about the Administrator

Description: This is not actually Chapter 4 specific, but probably the best time to do it in is early/mid Chapter 4.
- In one of your sectors with Waste policy on, let two small stockpiles fill up with Waste and wait for the protest event to pop.

- Destroy the Piranesi before it destroys a planet

Description: This is a Chapter 5 achievement, but you should actually start paying attention about being well-prepared after halfway into Chapter 4.

- You will be in a constant rush after late Chapter 4 and probably will not be able to re-establish vast supply lines and get this achievement at the same time.
- Install one or two more EVA Airlocks for repairs.
- Stock up on at least about 1200 Alloy.
- You will need about 600 Colonists ready to depart or about 500 Polymer stocked depending on the ending.

- Finish the chain of events concerning the strange spheres

Description: Science Event - PSR B1257+12F

- Find crew member.

There are two different endings and a difficult, rushy achievement here, so make a manual save right at the beginning.

- Finish the chain of events concerning the strange spheres

Description: Two events here, Vulcan must be done before Aventine.
1) Science Event - Vulcan

- Study the electromagnetic disturbances.
- Analyze the sphere.
- Naomi Protocol: Allow the team free reign.
- Leave the comet.

2) Science Event - Aventine
- Build the Natschach transmitter.
- Deploy the Natschach transmitter.
- Balance will be our doctrine.
- Leave the planet.

- Destroy the Piranesi before it destroys a planet

Description:
- Whichever ending (Remus or Romulus) you choose, you need to complete the game before our old friend Piranesi reaches Remus and destroys it.
- For both endings, you need to have 1000 tiles of Tiqqun covered with (any size of) batteries.
-- Tip: You can dismantle these back once Main Quest advances if you're low, but you need to have 1000 cells at one point.
- For Remus ending, you will need a new building and a 10-cycle process.
- For Remulus ending, you will need about 600 colonists ready to depart.


- Finish the game by following the path of Genetic Conatus

Description:
- Visit Remus.
- Meet the Ashtangites.
- Research and build their new building.
- Ignore the comms about Romulus planet and Edden being a liar.
- Adapt your whole crew (10 cycles) and finish the game.

- Finish the game by emancipating yourself from DOLOS

Description:
- Do not start the Remus event. Just go park at it and collect the science.
- Send a probe West of the star, discover Remulus and send a Science Ship.
- The P.A. will tell you that the crew is having hallucinations and that Remulus does not exist.
- After a while, you will get two different communications as events in the Tiqqun.
- Following these events, you will eventually disable your P.A. Edden and be able to interact with Remulus.
- Follow the Remulus line to complete the game and you will get this achievement.

- Replace Edden with the P.A. of the Protagoras

Description:
- Remember that we copied the Protagoras' P.A. in Chapter 2?
- At the very end, when you are asked to fly Tiqqun into the Piranesi, choose the "Replace Edden with Protagoras' AI" option.

- Build and disable your Mess Hall, set the game to maximum speed and wait till you fail, restart.
- Send a probe to almost directly East (very slightly South) of Moon to discover Unauthorized Access location and complete the events. (Just visiting might be enough, but the rewards are quite worth 30 Alloy during early game anyway.)
- Science Event Unauthorized Access: "Naomi Protocol: Create a temporary easement"


- Do not start the Neptune event before you find and complete the Saturn event.
- Saturn choice: Make contact > Break through the ice.
- Neptune choice: Use Oulixes' biometric data to open the sealed room
- Science Event Uranus: "Naomi Protocol: Cut down the tree"


- Set up an Alternative Life Center as soon as you can.
- Science Event Mack R: "Thaw the Ice" -> "Naomi protocol : Send a team"
- Science Event Tatra v8: "Naomi Protocol: Interrogate the P.A"
- Before starting the Fargo 39 science event, make sure you researched Exoskeletons upgrade in the Tech Lab under Science Ship.
- Science Event Fargo 39: "Deploy the entire crew in reinforced exoskeletons"
- Protagoras main quest event: "Naomi protocol: Save a copy of the Protagoras' P.A."
- Man is the Measure of all Things main quest event: "Naomi protocol: Meet the Elders"
- Science Event Rockatansky D79: "Establish infrastructure" - > "Descend to the cavity and study the sphere"


- Science Event Collapsed Food District: "Investigate the Animal Pens > Naomi Protocol"
- Shortly after you adopted the Dog, the P.A. will ask you whether to exterminate it for health purposes or keep it. Keep it and finish the game.
- Science Event Medical District Wreckage: "Choose Investigate the Research Facility -> Retrieve ZY6073" (All crew killed.)
- Science Event Cruc-P-43: "Use explosives" -> "Examine the sphere" -> "Study the concentric circles" -> "Leave the planet."


- In one of your sectors with Waste policy on, let two small stockpiles fill up with Waste and keep it that way.
- Install one or two more EVA Airlocks for repairs. (Chapter 5 Prep)
- Stock up on at least about 1200 Alloy and 500 Polymer. (Chapter 5 Prep)
- Have 600 colonists ready to depart. (Chapter 5 Prep)
- Have 1000 tiles of Tiqqun covered with any size of batteries. (Chapter 5 Prep)
- Science Event PSR B1257+12F: "Find crew member."


- Vulcan must be done before Aventine.
- Science Event Vulcan: "Study the electromagnetic disturbances" -> "Analyze the sphere" -> "Naomi Protocol" -> "Leave the comet."
- Science Event Aventine: "Build the Natschach transmitter." -> Deploy the Natschach transmitter." -> "Balance will be our doctrine." -> "Leave the planet."

- Visit Remus.
- Meet the Ashtangites.
- Research and build their new building.
- Ignore the comms about Romulus planet and Edden being a liar.
- Adapt your whole crew (10 cycles) and finish the game.

- Do not start the Remus event. Just go park at it and collect the science.
- Send a probe West of the star, discover Remulus and send a Science Ship.
- The P.A. will tell you that the crew is traumatic and having hallucinations and that Remulus does not exist.
- After a while, you will get two different communications as events in the Tiqqun.
- Following these events, you will eventually disable your P.A. Edden and be able to interact with Remulus.
- Follow the Remulus line to finish the game.

- At the very end, when you are asked to fly Tiqqun into the Piranesi, choose the "Replace Edden with Protagoras' AI" option.

These remaining 3 of the 17 hidden achievements are those I've neither figured out, nor could find any info about. They may be a) WIP, b) well hidden, c) deeply connected to eachother somehow or d) bugged for the time being, I just don't know.

According to SteamDB records, these have absolutely 0.0% percent completion rate throughout the community as well. I will update accordingly as they are solved in time. Please drop a comment if you happen to know.


What They Hide From Us
- Discover the ruins of the genetic facility
- Chapter: Unknown

I've tried scouting the locations instead of doing "the obvious objective" (avoiding too much spoilers) in Chapter 5, but no luck. (Surprise: Those choices all destroy the ship and kill all the crew!)

Update 23.12.2022: Found a few comments/reports that this can be triggered if you choose to follow the Remus ending and do the temple visits in a specific order, but no confirmation yet, might be randomly bugged.


Delivery!
- Research every single upgrade for the Drone Bay
- Chapter: 4+

I've completed every upgrade for the Drone Bay, but it did not unlock. Might be just bugged, or we might need to have found a Science Ship choice type of hidden upgrade for this earlier, which so far no one did apparently.