This achievement is for unlocking all of the profiles. Each character profile unlocks as you encounter them. In order to get all of the profiles, you must be playing in Extra mode (to have access to the Digest characters) and reach the True ending of the main game. If you do that, you'll naturally unlock all of the profiles.
At the end of the game, the last profiles to unlock will be the Chaos and the 5 Gods from the Digest mode, and Decimal which is unlocked by an event on the Boundary Plane.
The achievement unlocks when you go into the picture book and view the gallery.
Note that there is both a 'Profiles' and a 'Character Gallery' section. You only need to complete the first.