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The Fire Sword is in the Ice Arena. : ) It's on a shelf behind a wall on the right that can be removed by dealing with two levers on the left as you enter.
For the lever as you face north on the west side, throw a throwing weapon. For the lever in the south, hit it with anything.
There is another lever you have to hit first in the south.
Make sure the lever in the north is off before you hit it. That is, up. It needs to be off and you need to turn it on.
When you hit the lever in the south it should say, "Something happens."
And when you hit the lever in the north it should say, "A wall crumbles."
But if you first hit the lever in the north to turn it on and then hit the lever in the south, nothing will happen until you first turn the lever in the north off by hitting it and then hitting it again to turn it on.