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Listed here are all the story-related achievements. They are unmissable and will be given when you complete the required section

They are not necessarily listed in chronological order

Awoke with fragmentary memories after the crash of the Cassandra

Followed Salim’s Trail

Carried on with life, despite Salim’s fate

Followed the pilgrim’s trail to take refuge in the fort

Explored the inner fortress, and spoke to the doctor

Dreamed of Paris

Fired a cannon at the fortress gate

Found a way through the ruined cistern

Travelled through the desert

Took a walk in the park

Escaped the Shadow

Activate the alchemists’ device

Drained the fear and the life from a crew member

Activated a portal between worlds

Operated a scanning device, and learned of a child’s illness

Reached the doctor

Gave birth to a daughter, only to lose her

Failed to reach a child, separated by deep waters

Completed the story

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Achievements that are missable. Special cases marked with an asterisk (*)

Some are self-explanatory, others will have a short description of how to achieve them.

Kept quiet and still, and so escaped a predator’s gaze
When a ghoul is lurking around and looking for you, have it come near you or look into your direction and hold the crouch button to prone and lie still.

I got this naturally in the Cistern chapter (twice).

Took time to talk with an unborn child

Check in on the baby (pressing X) in 3 different chapters. Can get it as early as when you enter The Oasis (maybe bit earlier, not sure).

Tortured an innocent to aid an unborn

* Missable when Altruist (see below) has been completed. Reload a save to get the other achievement.

Near the end of the Laboratory level before exiting via the tram, you will need to assemble the equipment to extract vitae from a living person suspended in a chamber. Complete the mini puzzle to torture the victim and extract the vitae and go sit on the chair to inject it.

Spared an innocent, perhaps dooming an unborn child

* Missable when Torturer (see above) has been completed. Reload a save to get the other achievement.

Near the end of the Laboratory level when you have powered the tram, simply exit via the tram without torturing the person in the chamber to extract the vitae.

Found treasure beneath the water

Find the can of oil in the oasis. It's at the bottom of the oasis near the middle rock outcropping. The achievement popped for me when I moved the pottery that is hiding the oil, not when I picked up the oil.
screenshot:

Resisted fear, and resisted anger

Tied to ghoul progression of Tasi.

Needs more testing to get EXACT requirements, but consensus on surest way so far to get it is:

• In your entire playthrough, never succumb to fear during the resist mini-game (mashing WASD and moving mouse). When you don't resist, Tasi goes insane and runs to a predetermined 'fear' location where you 'respawn' after 'dying'.
  
• DON'T do the Harvester ending first (see endings section for details). I had a look in the game code and according to it Stoic should unlock with Provider or Iconoclast ending given you did the above point. I got it with the Provider ending.

I did some further investigation and found in the game logs there is some Ghoul Progression stat. It goes from 0 to 20 and if it is at 20 when you do one of the 2 'good' endings, Stoic doesn't trigger (according to game code).

Smashed lots of irreplaceable objects

I received this by just throwing around a lot of pots and vases. Could be around 20 or so pottery. Should pop around halfway through if you diligently smash everything you find. I got it in the Cistern level, pretty early.

Escaped a cage in the Arsenal without setting off a grenade

In the cage where you get the sulfur ointment, instead of blowing up the grenade, carefully remove the hook from the cage door. Then look to your right, and find the cage key on the body to open and escape the cage.

Left when things were getting interesting in Amnesia: Rebirth

When you enter the cave for the first time, proceed a bit further until you turn right into a dark corridor that has a torch at the end of it. Tasi cries out "Salim...". You can save and quit immediately after she says his name, that is how I got it.

Will try to confirm exactly how far you can proceed until the achievement doesn't pop any more.

Sent extra objects through the portal in the Alchemist’s Chambers

With the puzzle where you have to send the triangular stone to the adjacent room to power the portal on the other side via a teleporting device, send some of the cubes as well (you can use the machine multiple times, and there are some extra cubes on the back shelves). I think a total of 6 should pop it, otherwise keep sending them until it does.

Found an unfinished letter from an archaeologist to his sister

In the Fort building. When you get at the top of the elevator, go left and up the stairway. Keep left and look for some barricades. The note will close to it.

Collected notes to fill a journal

Collect 80 out of the 107 notes in the game.

This was bugged before the 1.04 patch where you could get it as early as The Dark World. But I tested again it with the 80 notes.

With a new playthrough after the patch, I unlocked the achievement only much later (in The Hunting Grounds). It unlocked when I got exactly 80 notes (I use the debug console to check this stuff).


Gazed at a reflection in the water

Outside the fortress main building, in the fortress courtyard, move around the left of the building. There is a little section containing a fountain. Interact to gaze into the fountain.

Found all the memories recorded by others

There are 17 cylinders in total. Please refer to this excellent guide for their locations:
https://steamoss.com/sharedfiles/filedetails/?id=2265491847

Found all Hank’s notes on the crew of the Cassandra

14 in total and you have to find each one in a single playthrough.
Refer to Mana's guide for a thorough explanation https://steamoss.com/sharedfiles/filedetails/?id=2265051390

Popped the lid on some carefully store meat

In the Cistern level you should find a grate in the wall that, when opened via a wheel, gives you this achievement. It's located in the sewer tunnels, in the last area where you can stand up to catch some air before the ghoul chases you.

Burned a forest’s worth of matches to illuminate dark places

Just use a total 120 matches by pressing R(tested). I got this in the Catacombs.

I found just over 180 matches so you should have plenty to use.

Completed the game faster than any Frictional developer

I completed this achievement with 2:19:37 on the game timer (debug console).

No official info just yet but the game code suggests it needs to be < 2:20:00, and this might possibly be the last one that you should attempt (it's pretty hard if you haven't played the game at least once).

There are various glitches you can search on YouTube, Twitch etc. that will significantly aid you. However, this can be done without any major glitches I believe.

I tested this with regards to the in-game timer:

• Exiting and reloading a previous save DOES NOT count against you
  
• Pausing (Esc) DOES NOT advance the time. Same goes for loading screens.
  
• Opening Inventory (TAB) DOES NOT advance the time

Collected all the other achievements.

Reborn seems to be quite bugged for some people. It didn't pop for me when doing my last achievement (Speedster). There is a very easy workaround (only using game code) to get that shiny 100% badge and I created one here:
https://steamoss.com/sharedfiles/filedetails/?id=2268551861

There you have it!

The guide should be fairly complete at this stage to allow you to easily get the achievements. I tested as much as I could, and thanks to all who contributed with extra info.

There are 3 possible endings, and each will give you an achievement.

Make sure to save and exit before doing anything with Amari so that you can reload a very recent save to do each of these in sequence. Otherwise, just load any of your previous saves and do the actions for each ending.

Left a daughter in the care of a god, and was reborn

Put Amari back in the crib. After doing that you should not be able to get her back. Then leave through the hallway and Mother will betray you.

Escaped to Paris with a daughter that must now be cared for

Do not put Amari back in the crib. Instead, take the leyden jar and exit to the hallway. Sneak past Mother to the door that you entered the room with. When you get to the starting area with the portal device, place the leyden jar in its socket and press the power button to activate the portal.

Sacrificed everything to cast down a god and end suffering

Do not put Amari back in the crib. Instead, take the leyden jar and exit to the hallway. Sneak past Mother and use the leyden jar to enter each of the 3 rooms connected via the power tubes to Mother. Each room houses a machine that you will need to destroy by filling the injector with a capsule and turning the lever.
Once the third one is destroyed, walk back to the boss room to see ending.