In kingdom hearts 2, how can i unlock the hades cup, the paradox one?

To open the Paradox Hades Cup (which is different than the Goddess of Fate Cup), you'll need to reach level 7 with Valor, Wisdom, Master, and Final Forms, as well as your summons. The final Cup is the Hades Cup, and it's brutal. It's 50 rounds long, and the rounds get exceedingly difficult, especially towards the end. Talk to Hades in his chamber to access any of these Cups once they're unlocked.