All of the following achievements are part of the story and can't be missed:

Out of This World
Find the UFO (Level 1).



Let There Be Light
Restore power at Norwegian camp (Level 2a).



Bad Blood
Administer a Thing test (Level 2b).



A Pale Imitation
Defeat the Rupture Boss (Level 4b).



A Thing of the Past
Kill the final boss (level 10).

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Ghost From the Past
Play the Tape (Level 1).



During the very first level you will descend into a snow pit filled with rubble. The audio recorder is hidden in the remains of a collapsed hut to the right.

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Perfect Trust
Achieve 100% trust with all team members in a single level (any level).
Killing Things in view of squad members, healing them, self-administering blood tests and handing out weapons and ammo increases trust.

Very easily done in the first level. You start with a full squad, and you will also find an additional pistol and ammo boxes for pistol and SMG ammo during the mission. Give the pistol to Weldon (the only suqad member without a weapon) and give every squad member ammo until they reach 100% trust in you.

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Colin's Fate
Find dead Norwegian (Level 2a).



In the same room where you encounter your squad engineer Carter. There is a frozen corpse sitting on a chair in the middle of the room. Approach it closely to trigger a small cutscene and the achievement.

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Audiophile
Find all tape recording save points.



There are a total of 26 save points in the game that you have to find and use (see level sections).

In order to access savepoint 19 in Level 8b, you have to bring the Engineer from Level 8a with you!

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Conspiracy Theorist
Find all hidden Gen-Inc. documents.



Initially bugged but fixed in patch 1.1. Old savegames work retroactively too. Popped for me at the end of Level 9b - Weapons Lab and probably requires interacting with all of the pc terminals.

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Remain Calm
Prevent any NPC from reaching maximum fear level in a playthrough.



The fear system is notoriously janky and underdeveloped in The Thing. Overall it's pretty easy to keep courage up and to get the achievement, so don't worry too much about it.

Fear rises most notably in horrifying enviroments like rooms with gore and corpses, but will quickly drop again if the squad member leaves the area that frightened him. Encounters with Things, especially larger ones / bosses, also rises fear. In an emergency, you can administer adrenaline syringes to temporarily boost a squadmates courage. Arming squad members with weapons will also make them more resilient to fear, depending on the potency of the weapon:
Sniper Rifle > Shotgun > SMG > Pistol

Squad members will communicate their fear level with verbal shouts and their facial expressions in the squad menu. At high fear, squadmates will start shaking their heads. After this, squadmates might eventually start to panic. This is indicated by a panic alert over their heads:



These alerts are the final hints for the player to get the squadmate away from the freightening scene or to administer adrenaline quickly. The panic alert will start yellow, followed by orange and finally red. Reaching yellow and orange alert stages doesn't effect the achievement, but red does.

Red alert means the squadmate has reached maximum fear and the achievement is busted.

• Achievement: Ghost from the Past - play McReady's Tape - collapsed hut in the pit
  
• Achievement: Out of This World - Find the UFO - unmissable
  
• Terminal 1: "I have compiled a 5-page report..." - Infirmary
  
• Document 1: Autopsy 1 - Infirmary
  
• Document 2: Autopsy 2 - Infirmary
  
• Document 3: Autopsy 3 - Infirmary
  
• Document 4: Autopsy 4 - Infirmary
  
• Document 5: Autopsy 5 - Infirmary
  
• Savestation 1: Infirmary Storeroom
  
• Achievement: Perfect Trust - max out squad trust before finishing the mission by giving every member a weapon and max ammo

• Achievement: Let There Be Light - Restore power at Norwegian camp - unmissable
  
• Achievement: Colin's Fate - take a close look at the corpse on a chair in the lab room
  
• Savestation 2: Lab Room
  
• Terminal 2: "We're all going crazy..."

• Savestation 3: Shelter
  
• Savestation 4: Supply Hut
  
• Achievement: Bad Blood - Administer a Thing test - unmissable

• Terminal 3: "Lost contact with the medi-center..."
  
• Savestation 5: Canteen
  
• Savestation 6: Comms Room

• Savestation 7: Sleeping Quarters

• Savestation 8: Ground Floor
  
• Terminal 4: "Gen-Inc personnel were here again.."
  
• Terminal 5: "I've positioned the telescope..."

• Terminal 6: "Controls for operating the crane..."
  
• Terminal 7: "Construction of the test chambers..."
  
• Document 6: Reminder
  
• Savepoint 9: Tool Room
  
• Achievement: A Pale Imitation - Defeat the Rupture Boss - unmissable

• Savepoint 10: Operations Room
  
• Terminal 8: "We have taken a number..."

• Savepoint 11: Observation Area
  
• Terminal 9: "Test subject B4..."

• Terminal 10: "Initial bio profile..."
  
• Document 7: Dr. M. Rodriguez's Note
  
• Document 8: Page from Hanson's diary
  
• Terminal 11: "All security gates are set..."
  
• Savepoint 12: Living Quarters
  
• Terminal 12: "I am getting increasingly worried..."
  
• Terminal 13: "Cell 1 - 829 Stenberg..."
  
• Terminal 14: "Terminal 747: Request access code for elevator..."

• Savepoint 13: Furnace Room

• Terminal 12: "Please can you check..."
  
• Savepoint 14: Study
  
• Savepoint 15: Control Room

• Terminal 13: "Demolition Staff Announcement..."
  
• Savepoint 16: Laboratory
  
• Terminal 14: "I've locked the grenade launcher..."
  
• Savepoint 17: Store Room
  
• Savepoint 18: Armory

• Savepoint 19: Staff Room
  
• Terminal 15: "When the troops arrived..."
  
• Savepoint 20: Generator Room
  
• Savepoint 21: Control Tower

• Savepoint 22: Guard Room

• Terminal 16: "Current tests on..."
  
• Savepoint 23: Storage Room
  
• Terminal 17: "The anti-thing virus..."
  
• Terminal 18: "Testing is going well..."
  
• Terminal 19: "Stolls was up all night..."
  
• Terminal 20: "We had what you might call..."
  
• Terminal 21: "Everyone was late..."
  
• Terminal 22: "I found a large hole..."
  
• Terminal 23: "The beast has friends..."
  
• Terminal 24 "Breath deep Blake."
  
• Savepoint 24: Robotics Lab
  
• Savepoint 25: Weapons Locker

• Savepoint 26: The Dome
  
• Achievement: Audiophile - will pop up right after interacting with savepoint 25.
  
• Achievement: A Thing of the Past - Kill the final boss unmissable
  
• Achievement: Remain Calm - Prevent any NPC from reaching maximum fear level in a playthrough - pops up after finishing the game.