I don't know the last quest, but the last boss is Jade Oni.
You have to beat the following areas to get to the next world:
Hametsu Village Crimson Fields Cave of Solitude Kishibe Village Shiritaki Temple Ancient Burial Grounds The Village Of Sorrow The Tree of Life Defeat Jade Oni Talk to Headmaster Talk to Cyrus Drake Defeat Cyrus Drake Dragonspyre
I'd regard The Key at Last as being the last MooShu quest, as that's the last quest given in MooShu, even if it's completed in Wizard City. One could also claim that Rematch is the last MooShu quest, as it has the same prerequisite as The Key at Last, but is actually done in MooShu. It's an optional side quest, though, whose only real point is to tell you how to fight the Jade Oni again if you care to.