Aquire Invisibility Cape Early:

There is a way to get the Magic Cape right after you get the Hammer in the Palace of Darkness(Dark World's 1st dungeon). In the graveyard in the Light World you'll notice there are dark colored rocks with the number 8 on the them surrounding a tombstone, but if you go to the same place in the dark world you can cut down a flower and dash into a pile of rocks that usually reveals a red ruby(worth 20 rubies). In this place you need to use your Magic Mirror north of the rock pile. If you've done this right you can circumvent the dark colored rocks in the Light World.

Note: You need to use the Magic Transprter between the Kakariko Village and the Lost Woods to reach this location.