Make your way through Chapter 6 - The Fall
Throughout the chapter, you will need to examine a total of 6 locked doors by pressing the X button on each door. Each door will have a short bit of commentary.
They will be in 2 sets of 3 doors each. The first set of doors isn't really hidden as you have to use a wall near them to progress in the chapter. They will be right after you ride a slow yellow elevator that is surrounded by some stairs.
The second set of doors is more near the end of the chapter, but more well hidden and missable than the first set. You will eventually come across a control room that has 3 seperate levels. You must use your portals to get up to the highest of the 3 rooms.
Once you're in that room. There is a half hidden door that you can pass through behind some cabinets. Go through that door and press X once again on the following 3 doors and as soon as you press X on the sixth door, the achievement will pop.
The doors DO NOT have to be examined in one playthrough
Refer to this video for exact door locations.