This skips the Elegy puzzle and the courtyard with the bombable floor.
If done correctly, the map room will load as Link passes through the shaft.
There are several ways to clip through the sun block. The methods for clipping here are the same as the ones in ISTT. Since this room has water in STT, it's usually best to clip as Zora.
This video was made in ISTT, but the clip works the same way in STT. All three setups shown involve rolling on a HESS frame.
It is also possible to skip the block by hovering up with 7 explosives and backflipping over the entire thing. However, if aiming to conserve explosives, it can be climbed in 6 by means of an angle change and sidehop at the end, or 5 by means of an angle change and gainer at the end. It should be noted that the 5-explosive is very risky as only 3 input frames are available to successfully complete the gainer to grab the block, as failing it would waste the explosives trying to be saved. Using 7 explosives is typically the best way to go about this block because the way to conserve explosives wastes more time than saving one extra explosive would grant. Do not grab the block as Zora Link at the end as you will be crushed by the low ceiling!
Line up with the diagonal wall opposite the compass chest, then hover once over the water to have a shot at the sun switch.
Pressing A to open the chest on the 1st, 2nd, or 3rd frame of the bomb explosion overlaps the small key get animation and text box with the fairy chest spawn animation.
This is a slightly slower alternative to the small key cutscene overlap strategy above, but it does not require bombs. To hit the crystal switch:
Backwalk from the chest and press B after falling to recoil off the wall. Hold right and press B when hitting the water to get a good angle and sink a little bit. Then, tap A and B in an alternating rhythm to preserve Link's height and the superswim speed while directing the swim with the control stick.
Stone Mask is extremely useful in this room and makes pretty much every strategy easier.
A 1st frame weirdshot can reach the crate from far away (first example in the video), and either a 1st or 2nd frame weirdshot can reach the crate from up against the wall (second example). This can be done on either side of the room, and similar weirdshots are possible for getting to the fairy chest behind the right sun block and from there to the right side crate.
Unlocking the camera on the first chu hover is easiest, but if you get to the top and haven't unlocked the camera yet, you can wait for a boe to arrive and target it.
As with the sun block in the previous room, the quickest way to get past the updrafts is to effectively skip all of them with a weirdshot. A 2nd frame weirdshot is best, but there are some positions where a 1st frame weirdshot can reach the chest.
When the hookshot it not available (such as in a Low% speedrun) recoil flips can instead be used to ride the updrafts to the miniboss room. To get across, a recoil flip straight across from the entrance of the door is enough to get a boost and land on a banister. From there, an aligned side recoil can be used to weave through the next 2 updrafts, all the way to the exit.
Drop the bomb near the flower and slash forwards to the edge. Turn right, then long jump holding left. Once Link hits the updraft, jumpslash and hold forward until the sword hits the wall.
0:52 in video. (Needs its own video with input display.)
This requires a 2nd frame weirdshot.
Hookshotting the fairy chest from very near the flames allows Link to open the chest on the first frame after reaching the chest. This frame perfect A press is on the 5th frame that the hookshot button has been released and ideally is timed. However, this can also be done pretty easily without timing by mashing start and A after releasing the hookshot. Since the pause menu won't come up if start is pressed while the hookshot is bringing Link somewhere, the first frame that either input can go through is the chest opening frame, so getting an A press on that frame will open the chest, and getting a start press and then pressing A during unpause lag will also open the chest.
Throwing a bomb to hit the crystal switch allows you to get very close to the chest before it spawns.