Stone Tower has perhaps the most complex dungeon design in any Zelda game. With two separate maps and a strong link between them, it becomes very lengthy, puzzling, and disorienting. Fortunately, through clever use of its design, it is possible to complete the temple very quickly under a number of various circumstances, skipping large portions of the level.
Under normal circumstances, it is usually required that one has the Elegy of Emptiness and Mirror Shield upon entering the temple. That is, outside of the temple, the Mirror Shield is only needed to obtain the Elegy, and that the Elegy is only needed to enter the temple. However, it is actually entirely possible to enter without the Elegy (refer to this page), so being able to complete the temple without these items suddenly becomes very important to skip a large section of the game. In a playthrough that aims to get everything, the Light Arrows in the temple greatly speed up aquiring the Mirror Shield and Elegy, so under most circumstances it is much better to complete Stone Tower without them.
When aiming to complete the temple, one only needs to visit the normal orientation of the temple once, so it is important to get everything needed before ever inverting the temple.
When entering the temple without Elegy, it becomes impossible to get past the first room on the left. Fortunately, nothing is of use in that elegy puzzle, so there is no reason to ever do it. In order to progress, one must bypass the sun block in the first room on the right.
The fastest (and most explosive-conservative) way to do this is by using the explosion of a well-placed bomb to boost you through the corner between the block and the wall on the left. To do this:
If done correctly the explosion from the bomb should clip you through the wall.
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!
After the first locked door comes an obstacle that is usually tackled by using the Mirror Shield on the mirrors. However just like with the first sun block, this sun block can also be skipped, this time with either a weirdshot or hovering.
This is, by far, the fastest and simplest way to skip the sun block. Run over to the upper right portion of the room (the upper left should work as well) and preform a weirdshot with the hookshot. Hookshot to one of the crates on either side of the sun block, and you are free to proceed. Before weirdshotting, you may need to kill some of the Black Boes, as they can often get in the way.
This block can also be skipped with 7 hovers like the other, but it is possible to consistently save 2 explosives on this one, so that is what is usually used. After 5 hovers up and an angle change, it is possible to grab the top as Zora Link, thanks to the higher ceiling. The Black Boes here can get in the way easily, so it is recommended to either quickly kill them first, get ISG at the beginning of the room, or wear Stone Mask if it is in possession.
Although not directly related with skipping the Elegy, when aiming to complete the game, one may bottle dupe over Deku Mask after it becomes useless for an extra bottle. If this is the case, the updraft room provides an obstacle to completing the temple.
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. However unlike the previous weirdshot, it is both easier and faster for this one to advance two frames after pressing the hookshot button, since this will put you on the same level as the chest you want to hookshot, rather than at an awkward angle below it.
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.
After defeating the Garo Master and obtaining the light arrow, it is important in a speedrun to return to the entrance of the dungeon so that you can shoot the red crystal and invert it. Though both the Song of Soaring and Deathwarping are viable options, deathwarping is typically preferred, both because it is convenient to take damage from the Garo Master (each of his attacks deals a heart of damage), and in the situation that the Song of Soaring is not an option (such as in a Low% run).
Once light arrows are in possession, the mirror shield becomes obsolete, as all sun blocks or symbols can be destroyed or activated without needing a light source. After inverting the tower (refer to this page), a great part of the temple can be skipped using 1 of 2 different tricks, rendering Elegy useless as well.
Following the right path at the entrance, make your way to a chamber with a floor switch and dex hand. In the distance, an Eyegore can be found, usually only accessible through an extra key and hookshotting a chest that is supposed to be activated later. To get to this bridge from the chamber, a well-aligned bomb recoil flip is enough to cross the gap. It is important to kill it and have the Giant's Mask chest appear.
If doing the recoil to Eyegore Bridge method of completing the temple, it becomes necessary to grab the boss key. To get there, hookshotting the key chest, recoiling down there, or a sidehop jumpslash by the dex hand is enough to make it. To get back, a precise hookshot can be used to latch on to the Giant's Mask chest with the boss key in hand. The best spot to do this is just outside the door leading to the blue bubble corridor, in the bottom-right corner (relative to facing the bridge).
It is possible to immediately make it to the bottom floor of the Eyegore bridge room by entering the door on the left side of the beginning of the inverted temple. This gap can be crossed with 1 explosive, without hovering at all, using a long jump:
Alternatively, you can use 3-4 hovers to make it to this ledge.
In the room under the Eyegore bridge, there is a balcony with 2 enemy pots on it. At the spot where the edge of the balcony intersects the invisible wall bounding the room, there is a small spot where you can clip out of bounds and hover directly to the boss room. To get to this spot, there are two main procedures you can take:
Aim at the out of bounds spot from the corner of the platform closest to it, then turn around and get ISG. Do 4 hovers holding down-left toward the platform, making sure to Z-Target a chu on the second hover, then change angle toward the out of bounds spot. Hover out of bounds, avoiding the pots, then keep hovering toward the loading zone. This method is considered extremely difficult, and is usually only recommended for a segmented run.
This method is generally safer than the previous method, as there are less obstacles preventing you from getting out of bounds. Go to the same corner of the platform as in the first method, but walk up the slope to your left and recoil flip to the balcony. Destroy the pots, then do a hover down off the balcony. Pull and shield a chu while sidehopping left, change your angle toward the out of bounds spot, then hover down below the balcony and up toward the out of bounds spot. From there, just hover to the loading zone.