In Kingdom Hearts: Birth By Sleep for the PSP, there is a secret boss called Lingering Spirit Vanitas that you can unlock in different ways depending on the mode you’re playing on.
Beginner Mode – Not possible to unlock on this mode
Standard Mode – Complete the story mode for all three characters, beat the Last Episode, and collect all of the Trinity Reports
Proud Mode – Complete the story mode for all three characters, and beat the Last Episode
Once unlocked, you’ll see a portal in the Keyblade Graveyard. Inspect the portal and select the second option to start the fight.