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I'm a bit stuck here. I've got the fire bubble and the ice bubble, but can't find either sword.
I also can't get back into the Arena of Fire, because there's an unkillable bat (at least until I have the sword) now blocking the entrance.
In the Arena of Ice, there's a switch on a wall which removes another block of wall so you can access the bubble.
Then there's another block of wall behind which I can see a shelf hidden, but nothing removes it. There's a second switch across a chasm, but arrows and spells don't trigger it/lower it.