How do you unlock any paradox cups in kingdom hearts 2

I like thisgame, but I haven't played it for a while. Although I'm pretty sure you just go to the Underworld and talk to the little pink guy and he brings up a menu where you can choose a cup to enter. Then you beat all the enemy's in the rounds and you should have a new cup on the shelf near the pink guy. You can also see the rules and how many matches there are when talking to him. But to unlock them altogether you finish the game until you finished (I'm not sure but I think The Little Mermaid or The Lion King) world. (you might have to return to the world to fully complete it)