In order to get the Labyrinth achievement, you have to pass through each room only once and then pick the correct door to exit. You have to pass through the rooms in this exact order:

• The room with the paintings (other guide calls it battery room) this is the only starting spot
  
• The room with the book shelves
  
• The room with the projector
  
• The room with the TVs
  
• The room with "We are science" written on locked doors (final room - you've through the labyrinth, just continue out)

To do this there are four sets of doors that you need to choose between left and right, which I will refer to as L (for Left) and R (for right).

There are 16 possible combinations that can give you the achievement and the game picks one randomly each time you play or load a save. These are:

L L L L
L L L R
L L R L
L L R R
L R L L
L R R L
L R L R
L R R R
R R R R
R R R L
R R L R
R R L L
R L R R
R L L R
R L L L
R L R L

Save the game before you enter the door with the bright white light. I think it auto saves but it's best to be sure. Pick one of the patterns above and follow it. If at any point you do not go to a room in the sequence above, load the save and try again. You can't go through the same room twice and get the achievement, so if you find yourself in a room you were in before, load the save and try again.

I picked one pattern and kept trying it until it was the one that was randomly selected by the load.

If you see the room with the paintings a second time, it considers that you have restarted the labyrinth and you can't get the achievement. I think that's true of the other rooms as well. And if you do make it through in more than the four moves (and don't get the achievement), it's auto save overwrites your save so you have to replay to try to get the achievement. So if you want the achievement, it's better to load right away if you are seeing a room repeat.

I choose L L R L because someone else said it worked for them. I had to try it a number of times before it was the one randomly selected and I got the achievement.

This was in the discussions, and it seems to have worked for some, but it didn't work when I tried it:

Originally posted by Comfortably_Numb:

For those who still struggle to get the labyrinth achievement, here's how it works :
When you open the door to enter the labyrinth, pay attention of the first turn (right or left) on your way. If it's right, then take the right at the next door and do the opposite if it's left. Repaet it after every door and you will beat the labyrinth in no time. I've tried several times in a row and it worked every time for me

It's as good a way as any to choose which of the 16 paths to pick, just take note of which rooms you go to and if you see one twice, load from save and try again.