moon/post-moon story recap

[Illya]

hi, could anyone give me a recap of what happens during the moon (you beat up kaguya but I don't remember why) and what happens up until there's no more story?

and also if the Hillary npc does anything significant?

[Dark Deceiver]

Hillary remains useless, much like the real life version.

You beat up Kaguya because she gets possessed by a dress, and currently we're trying to stop a boat from being used as a weapon against Earth. May have something to do with Susanoo and Amaterasu's brother, Tsukuyomi, who got name-dropped a lot.