Achievements will unlock once the game is exited, don't be alarmed if you don't see them pop up while you are playing

You don't need to see identification
To do this, in the Main Menu, open the locker and grab the key with the head on it, stick it in the 1st slot on the Module board, this will also allow you to skip setting the player height and floor level everytime you open the game

Unlocked the Museum Basement Sandbox
To Unlock this Module go to the Breakroom level, throw all the items into the Archive bin

After that continue on to the Museum level and there will be a wall on the left hand side of the corridor before the 1st puzzle room after the tutorial area, the door will now open when pushed

Smash the box inside for the Module

Throw the Module in the bin before the gun training area and then finish this level

After that you can exit to the main menu and smash the box to get the Module and place it on the Module board on the bottom right slot

Enter the Voidway
This will unlock during Story Mode, after the Time Tower level

Click all the buttons!
Click all of the buttons in the Museum level, there are 34 of them in total, this includes the 6 on the item vendor, the 3 holding the statue up, 3 in the time room, 2 for the elevator, 2 behind doors and the rest are obvious

Here is a video that shows them all, credit to DeVour:

Kill 100 headsets in Arena without dying
After completing Story Mode you will unlock the Module for Arena Mode, you have to kill 100 headsets in there without dying

Beat the entire arena
Unlock Arena mode by completing Story mode, after that you need to complete all the challenges, Trials on hard and Clear up to Round 10 of Survival in Arena mode

If you die in Survival mode, you can click Resume to carry on from the round you made it to, you don't need to clear all 10 rounds without dying

Unlock redacted chamber
Unlock it from the Museum level, it's in the box next to the 1st reclamation bin

Recursion through [REDACTED]
Get the Handgun Course Module and jump into the darkness one more time after putting it in the Reclamation bin

See video:

Complete the handgun course
You just have to complete the Handgun Course, you time doesn't matter, my hand got stuck while climbing so my time was over 10 minutes and I still got the achievement

Back to Tuscany
The module will be sat on box waiting for you after you leave the handgun course, can't miss it, just put it in the reclamation bin and finish the level

Unlocked Zombie Mode

Survive Zombie Warehouse
Must be on Hard difficulty

Make it to round 15 on survival on hard or greater difficulty

Unlock all doors in lockout mode

Unlock Hover ship

Unlock The Hover Junkers module