Simply complete all seven memory sequences and the achievement should pop. You don't need all the fragments for this achievement, however for the "true ending" and the "Breaking the Loop" achievement you will need all the data fragments and then just replay Memory Five to reach the second gateway via a golden bridge.
Edit: I made this solution at a time when nobody else had completed the game, it's simply to verify WHAT one of the secret achievements was and the basics on how to unlock it. Just beat all seven levels, that means walk through the doorway at the end of each memory...straight-forward levels and there is no punishment for failure except for going for the River Styx achievement or the Impress Warren Vidic one.