How do you unlock each cup in kingdom hearts 2

Pain and panic cup: after the second victory over Pete at Timeless River
The Cerberus cup: when the first episodes of Agrabah, Halloween Town and Pride Lands have been completed

The Titan cup: After defeating Hades

The Goddess of fate cup: After completing the first three tournaments and the first battle with Xemnas in the World That Never Was

Pain and Panic paradox cup: After completing the four normal tournaments

Cerberus paradox cup: Form levels for Valor, Wisdom and Master form have to be at least 5

Titan paradox cup: Summon level must be at least 5

Hades paradox cup: After completing all other cups and hollow bastion has been renamed radiant garden. Also, all form and summon levels must at least be 7