Instructions
Unlock all other cups. You will not be able to participate in the "Titan Paradox Tournament" until all other cups have been unlocked. Most cups are unlocked by completing the main story. The "Cerberus" cup may be obtained by completing "Halloween Town", "The Pride Lands" and "Agrabah." The "Pain and Panic" cup is earned by completing "Disney Castle". "The Goddess of Faith" cup is unlocked when you win the first battle against Xemnas during the story and earn the other two cups.
Level Sora's "Summon" ability to at least level five out of seven. Leveling up the summon level may be done by using a "Drive Point" when a creature is summoned. "Drive Points" are used once the "Drive Gauge" is completely filled. The "Drive Gauge" fills up based on the amount of damage Sora takes in battle. A summoned creature increases the experience for all available creatures, however, only one experience point is earned per summon, so it will take time to increase the summon level to five.
Visit the Underworld and enter the large blue door leading to Hades' chamber. Speak to Hades and he will allow Sora to participate in the Paradox Cup Tournaments. Choose the "Titan Paradox Cup" to participate in the Titan Paradox tournament.