Umm, no, you couldn't be further from the truth.

Seal 100 Acre Wood
Seal Atlantica
Finish the Goddess of Fate cup
Twilight Town: Sunset Terrace
World that Never Was: Brink of Despair
Space Paranoids: Central Computer Mesa
Get one each of all of the Synthesis Materials

(I forgot it in my thread)

Either way, to activate the Hades Paradox Cups it's required that all of your Summons and Drives are high levels (preferably level 7).