The solution to this achievement is fairly self evident – make sure the “Uncovering the Truth” challenge is selected before starting the mission, find all the documents, and the achievement pops.
A map for all the documents can be found on a guard tower right next to the large central building just to the southeast. Approach the guard tower from the south.
Currently, there is a problem with the 360 version which makes this achievement tricky to get only on the 360. One of the documents is on a tower structure just east of the pipes that run to the central building from the south. There are some climbable (white) walls on the structure and a short ladder segment hanging from the high part of the structure but the map is flawed such that Lara won’t grab the top edges of the climbing walls or the ladder segment as she should. (On the One, she will grab these as you would expect.) To climb the tower structure on the One, you climb an adjacent tree and jump from the highest branch to the ladder segment. However, because she won’t grab the ladder segment on the 360, you can’t climb up and get the document on this tower structure (or at least I couldn’t find a way to climb up).
You do have an opportunity to get this document after you shut down the south tower and exit onto the roof. From the roof, you can fire an arrow to the tower structure with the document and zipline to it. Just remember to jump off onto the tower structure before you automatically transition to the second zipline. From there you can drop down to where the document is. As far as I know, if you don’t use this opportunity to get this document there is no other way to get it until they fix the map.
Let me know if you know another way to climb up the tower structure with the document on it.