On the snow mobile when on the snow plains, hold x and tap circle until a new screen shows up. This screen is a mini-game: get as many matches as you can to win prizes!
-Soul of Rebirth
In Final Fantasy II on the PSP, you can unlock Soul of Rebirth if you have beaten the game once. Soul of Rebirth allows you to play a separate scenario with Minwu, Josef, Scott, and Ricard. This is made to be a challenge, as the time put into this scenario will mainly be from making your characters stronger.
To unlock extras in the game (an art gallery, a bestiary, and a music player), simply beat the game.