Death Mountain Descent will allow you to explore all of Dark World without obtaining the third pendant, the Master Sword, or defeating Agahnim.
First, you'll want to get the Moon Pearl out of the Tower of Hera. That's necessary unless you want to stay as a bunny the entire time. Once you've acquired it, exit the dungeon. Now hop in the teleporter just outside the Tower of Hera and go to Dark World. Hop down the cliff, and make your way to the right. Go to where the broken bridge used to be in Light World.
Now stand right under the top statue, as far against the wall and statue as you can get. Mirror to Light World. This is the tricky part, you must move ONE PIXEL to the right. No more, no less. If you don't do it correctly, you have to start all over. After you've moved, wait until you get teleported back to Dark World. You should be ONE PIXEL closer to the ledge now. Now DON'T MOVE! If you move, you will have to start over again. Mirror back to Light World.
Now walk to the right until you're stopped by the bridge post. Wait until you stop flashing, and hold down the B button until your sword charges up, while still facing right. SLOWLY move backwards into the sparkly teleporter. If you don't do this slow enough, the trick won't work. When you teleport, if you don't get teleported back to Light World, you did the trick correctly. Now press right to jump off the cliff into the black stuff. Make your way around the black stuff and to the bottom of the screen.
Go down one screen and you'll be on top of a cliff in Dark World. Hop off the cliff and you're now allowed to explore Dark World! If everything is glitchy, enter a cave, then exit and things will be normal looking.