Instructions
Go to Disney Castle and successfully clear the level. This will unlock the "Pain and Panic" Paradox Cup, the prerequisite for the Cerberus Paradox Cup.
Wait for the notification that informs you of the "Pain and Panic" Paradox Cup. Return to the main screen.
Raise all of Sora's forms to at least Level 5, excepting his Final Form. Sora changes form by fusing with another character. He can only obtain a certain form if a character is in his party. Raise the levels by replaying levels in all of Sora's forms until they reach Level 5.
Talk to Hade in Hades' Chamber. Select the Cerberus Paradox Cup to play the battle mini-game.