Well since you've beaten the Swamp Palace, that means you have the hookshot. Exit the Swamp Palace (in the Dark World), and head North East until you find a broken bridge. There, you will find a purple post, a large boulder, and a skull. Get rid of anyone of them in order to go just a little bit north. On the left side of the ledge you should see an opening (an opening where Link could jump down into the river). Don't jump! Simply use your hookshot across the river (you'll latch onto one of the two skulls that's lying on the other end of the river). And from then on, you can move westward

Oh! And as for why you're recieving too much damage, well...without revealing any future information on the game, you'll find more items to help your defence

-BGS