When you clear the game DLC (The Lost Archieve) for the first time, you will automatically unlock the Loop ending (and unlock the trophy related to it). The game will reset you back at Memory 1. To get out of this "Loop" you must collect all 20 decipher fragments (by using DNA Memory select). Once you nab the 20th, a message pops up on the screen saying "LOCATE THE BACKDOOR".
Once you've received this, you need to restart Memory 5. You'll notice a new cut-scene during the intro showing a new bridge waiting for you at the very end of the level. Play through the whole level again, and when you get to the end take the new bridge which leads left off to a previously inaccessible doorway. This will "break the loop" and lead to the end credits.
If you are diligent in your first playthrough, you can get all 20 data fragments before finishing the game. You will still get the Loop ending, but can then immediately load up Memory 5 and get this trophy.