You've got a good way of thinking about it, but Goddess, Doom, and Poltergeist aren't the three tiers of the final battle, they're the three Statues. Which kinda gets confusing, because if they're the three statues, I don't know how you can beat them all and still use magic until the end of the tower. But I dunno, maybe I'm the only one confused, and I got it all wrong.