To perform this, get a statue and throw it to the corner. Get on the top of the pillar using a backflip and leafe and walk off the edge of the pillar slowly so that you grab the edge instead of jumping off. Now tap Left and Link should go through the wall. Now Climb up and adjust your angle to jump out of bounds, then use the Leaf to fly to the hallway with the door leading to the rest of the dungeon.
From the entrance, go right onto the ledge. Hop onto the pillar near the hut where you place the statue, then Deku Leaf over on top of the hut. Climb to the peak of it, and wait until the water is about to rise. Facing the entrance with water pouring out of it, backflip and pull out the Deku Leaf immediately. Glide over through the waterfall, and release the Deku Leaf when you're up against the front of the entrance when the water is raised. If done right, you'll be sucked inside.
Using a slow superswim, it is possible to simply climb the ledge behind the waterfall, skipping the beginning of the temple. This is most useful in a TAS.
After placing statues on the right and middle switches, roll over the left switch, and you will land of the rising platform as the cutscene begins.
After you picked up the second statue on the first floor, you are supposed to use the Command Melody to jump him over a bridge you get from standing on a switch. Instead of doing this, you can walk with the statue to the ledge on the same side as the switch. Walk up to the pillar which stops you from continue. Walk slowly until Link's body is almost halfway over the void, then pause, let go of the control stick, and unpause. Now go into first person mode and turn right until the B button GUI is lined up with the black texture as seen in the video below. Then perform a sidehop to the left.
Simply glide to the rising platform and jump to the small key chest. To get back to the door quicker, jump into the abyss and you will death warp back to the door.
Place one statue on either of the scales. Jump off the ledge by the opposite scale and glide to the scale's far edge with the deku leaf. Fall, roll, and grab the ledge of the platform. It is also possible to get to the ledge using only leaf pumping, but it is more difficult.
Put two statues on one of the two scales. On the opposite scale, while holding the goddess statue, sidehop back and forth until the scale reachs the appropriate level, then proceed to the next room.
Get on the block in the middle of the room and glide to the golden ledge on the left side of the lasers. From here, glide and grab the ledge of the statue. "Call" the goddess statue, then immediately glide back over the lasers.
Using an Item Slide, you can simply bypass lasers if you have enough speed as lasers are considered an actor.