Unless you are a purist, use emulator save states. Some rooms in Parallel Worlds feature "pixel-perfect" movement requirements or invisible traps.
Your first priority should be obtaining the Magic Hammer. It’s hidden in a cave in the Parallel World’s version of the Lost Woods. legend of zelda parallel worlds walkthrough
Before hitting the main dungeons, you need to survive the overworld. Unless you are a purist, use emulator save states