Ride the rising platform up to the second level and jump to the ledge. The easiest way to align for this trick is to stand on the ledge, facing the Dodongo skull, with the camera on the front of Link and let it pan out until you can see the bomb chest. Once you've aligned with the chest, hold L and walk over to the green pillar. Position yourself as in the video, and do a jumpslash. You will recoil off of the green pillar and land by the chest (this will cost you 1 heart). Because of the convenient layout of this dungeon, you can now simply light the Dodongo Skull's eyes and proceed, skipping almost all of the dungeon.
Note: If you are completing this dungeon as an adult, Link's height will be enough so that he can simply grab the ledge to the chest from bellow.