From the end of the bridge, pull out the Gale Boomerang and target the collumn towards the left side of the door and do a long jump attack. From here, climb onto the fallen boulder, and target near the torches on either side of the door and use another long jump attack to reach the next plaform.
By using the Boomerang it is possible to throw a bomb against the pillar on the ceiling making it drop down. This leads the way to the Water bomb chest up there.
Right before the bomb hits the pillar, jump attack to get on the platform and save time.
One time consuming task that occurs in the Lakebed Temple is emptying your bomb bag of normal bombs so to obtain water bombs from chests. Instead of throw the bombs into a body of water, head over to one of the waterfalls in the stalacmite room. By standing under the water while trying to pull out bombs, the bomb's fuse is put out immediately allowing for incredibly quick disposal.
From the entrance to the swiveling staircase room, head over to the top of the staircase and pull out the Gale Boomerang. Target once just right of the chandelier on the ceiling and twice on the spire of the ceiling over the switch. Long Jump onto the staircase's banister as soon as the boomerang is over the chandelier and then over to the ledge. This is a lot faster than have to move the staircase multiple times.
It is possible using long jumps to get the clawshot much earlier than was intended without ever having to go to the second floor of the dungeon and change the water level. Go to the hanging platforms room and run to the ledge of the top platform. Pull out the Gale Boomerang and target above the doorway on the left. Use a double long jump to jump to the hanging platform, and then to the door.
After doing the above trick you can get over the railing in order to get to the deku toad faster. Jump attack on top of the opened chest (grab the Small key first for Gate unloading) and pull out the Gale Boomerang. Target slightly to the right of the pillar. Now simply use a long jump to get onto the railing and blow up the rock if you have bombs Else you will have to clip through the rock as explained below. Timing is rather strict. You want to LJA as soon as possible or you will overshoot.
Please note there the current routes do have bombs at this point and don't need this clip.
With a pot from the cave right next to the rock you can clip through the rock and proceed without a bomb. Get the pot from the small cave using Iron Boots and put it down as close to the rock as possible. Now swim up and then down in between the rock and the pot to get slowly pushed through.
In the current Any% route you want to do the preparation for Gate Unloading in CitS later so you backtrack to the main room.
Here you can use the clawshot to take a shortcut up to the East wing and skip turning the bridge at all. Clawshot right towards the stairs, go up about 7 steps and clawshot the vines on top right to get to the East Wing.
It is possible to clip into the bridge by standing on the edge of the barrier and falling down onto the seam, from there with a perfect angle you can backflip the bridge to the mid-point. You can then clip inside the boss room.
Clawshot up to the chandelier standing right next to the switch. Drop down, make a step to to right and sidehop.
After landing on the pillar, walk up and position yourself as shown. L-Slash slowly (don't mash!) until you drop down and backhop.
Then charge a spin attack and carefully go left until the outer end of Links beltbag touches the wall. Release the quickspin, backhop three times, let go of L and hold up-right to clip into the Boss Room.
If you land onto the Boss room your backhops weren't exact, hold down-left to clip then.
In the western gear room, It is possible to skip having to activate the gears to grab Heart Piece #10 with 3 LJA's (on the third you'll want to wait for the Boomerang to be completely through the wall and then immediately Long Jump)