Everytime Story mode is successfully completed a Bonus Character will become unlocked. To play as the character hightlight Squall at the 'Character Selection' screen and enter the following codes to unlock the corresponding character.
Complete Game 3 Times - Cid: L1
COmplete Game 4 Times - Mumba (Final Fantasy 8): L2
Complete Game 5 Times - Cloud (Final Fantasy 7): R1
Complete Game 6 Times - Cactuar/Cactrot: R2
Complete Game 7 Times - Aya (Parasite Eve): L1 + L2
Complete Game 8 Times - SD-style Chocobo: R1 + R2
Complete Game 9 Times - IbenSuper Airship: L1 + R1