Purchase Dissidia 012: Duodecim [prologus] Final Fantasy from the PSN store. When at the installation screen, download the file with the the data for Aerith to your Memory Stick. Start Dissidia 012: Duodecim Final Fantasy and Aerith will be a selectable assist character.
Battle Replay
Successfully complete Main Scenario 012.
Fight as Desperado Chaos
Finish Main Scenario 000 to unlock secret character Desperado Chaos.
Fight as Gilgamesh
Finish Report 08 (6) with Bartz to unlock secret character Gilgamesh.
Fight as Prishe
Finish Report 08 (2) with Shantotto to unlock secret character Prishe.
Fight Feral Chaos at the start
During the tutorial you will be asked by the Moogle if you have already mastered Dissidia. Answer "Yes" to battle against a level 130 Feral Chaos with a level 1 Lightning. If defeat it, it will be automatically unlocked in Free Battle mode.
Museum
Successfully complete Main Scenario 012.
Original Dissidia story
Successfully complete the game. An option to play the original Dissidia story will appear at the "Story Selection" screen.