This is unlocked near the end of Case 2 - A Study in Green:
After Completing the Mayan Temple
You must ensure that the clue 'Albeit's Lies' is active instead of 'Albeit's Truth' as this will open up part of the conclusion in which will allow you to interact with the temple within the globe to start the reconstruction.
The achievement is very difficult and involves solving several challenging puzzles. Video Guide below:
After finding a missing piece of the globe in Albeit#s residence, you must return to the Club House. Insert the missing piece and the Globe will turn into a Mayan Temple.
Holmes will now re-create the journey of the 4 friends in order to deduce events.
** I have been told that you can skip all puzzles except the last and still get the achievment** confirmed by commentsPhantasmagorical Journey:
Puzzle 1 Floor Puzzle
Forward, left, forward x 2, left x 2, forward x 3, right x 3, back x 2, right x 3, back x 3, right x 2,forward x 5, left x 3, forward x 2, left x 2, Forward.Puzzle 2 - Lever Puzzle
There are 6 columns each with a lever. You must turn the levers in correct order to reach handles which unlock the next path.
As you stand facing the columns, think of column to your left number 1 and the column nearest your right number 6. Sequence:
Lever 4,- Handle 1
Lever 6 - Handle 2
Lever 5 then 3 - Handle 3 3
Lever 2 - Exit (May need to turn more than once)Puzzle 3 - Boulder Dash
Run down the path taking cover from a boulder, make sure the cover is not blocked. The boulder travels back up the path so you will need to avoid it twice.Puzzle 4
- Collapsing Floor (This took me around 30 minutes to solve)
There is a lot of backtracking it is not a straight forward path. Therefor it is difficult to describe. After getting your way to the top of the right side of the exit, you must bactrack down the middle, almost back to the beginning. You then travel up the left side of the wall. When you reach the very top, you will have to turn around, run down the same path, turn into the middle and run out of the exit.
Very difficult to explain - Major backtracking involved. Check out a video at the end if you cant figure it out. Puzzle 5 - Poison Maze
Very easy compared to the nightmare that was the last puzzle. The room is filled with Mayan Portraits. If the portrait is Smiling then it is safe to pass. If the Portrait is frowning (& red) then you will be poisoned to death.
Head to the left side of the room, you will need to briefly backtrack to the center, but keep on heading left. Avoid any Red Frowning Faces.Puzzle 6 - Calendar Puzzle
There are 10 buttons in the room with the Mayan Calendar and Statue. Number the Buttons 1 -10 with the button nearest to you from entrance(facing the locked gate) 1 and the button to your right 10.
1, 6, 3, 8, 10, 5, 2, 7, 4, 9
After solving the riddle you will reconstruct what happened in the temple. You will appear back at the club and the achievement will pop.
Video thanks to TetraNinja and covers the full Temple Run