Magic Armour Quest
First, you need to go to the Malo Mart in Kakariko Village and contribute a total of 1000 Rupees to the elder Goron on the left - this will repair the West Bridge in Castle Town. Then you'll have to donate another 2000 Rupees to finance a shop in Castle Town - you can get the Magic Armor there for 598 Rupees!
As for running with the Barrel of Hot Spring Water - it has a bit to do with luck, it took me a few tries - just keep running and hope the birds and ground guys don't come after you. Anyway, go East, make your way to the West side of Castle Town and throw the Barrel at the Goron laying there to get a Heart Piece and open a Shop on the Southern Road!
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