The dungeon boss strategies are covered on their respective dungeon pages; see the following links:
This fight is straightforward; if you jump on its head, it will not shake you off before you can hit the spike in. So follow this plan:
The second Imprisoned fight is the most difficult boss fight in the speedrun. There are two main parts to the fight: getting on its head quickly, and staying on its head permanently.
The fastest way to get on the Imprisoned's head is to immediately destroy all the fingers on its left hand. To do so, when the fight starts, sprint backwards for about a second, then turn and do vertical sword slashes while Z-targeting. If done correctly, all the fingers will be destroyed, and the Imprisoned will retaliate with a charged attack. However, while it is charging, the first air vent will be active, and you can ride it up to the next level.
Once on the next level, you must be careful about getting onto its head, as in many places it is still to high to jump onto. You can either wait and be cautious, or run backwards slowly until it finishes its charge attack, then jump for the head at that point.
To stay on the Imprisoned's head, we will use a jumpslash to avoid the cutscene where we are thrown from the beast. Get the first two hits using a vertical spin attack, then take a small step back and pause for about a second. Then do a manual jump forward with an immediate jumpslash. If timed correctly, the jumpslash will hit, but the cutscene will not immediately play. Use these couple seconds to position yourself close to, but NOT on top of, the sealing spike. The cutscene will begin to play, but Link will not be performing his unsteady animation.
After the cutscene, pause for a beat, then repeat the above. If done correctly you will stay on the head again during the ensuing cutscene, and can deliver the final three blows quickly before you are thrown off.
If the fight goes wrong, you can use the Groosenator to help you stun the Imprisoned and get back on its head that way, then try to resume the jumpslash strategy if necessary.
When you're using the Groosenator in the second two Imprisoned fights, you can avoid watching the shot fly by pressing B right after pressing A. This allows you to move Link around while the shot is flying, enabling you to get into better position.
During the Levias fight, it is possible to skip destroying the eye tentacles and trigger the second phase early. However, Bilocyte will be invisible for the second phase, since the game hasn't loaded the appropriate data. This can be done by running next to Levias' blowhole and doing a horizontal spin attack at the right angle. This will hit Bilocyte and cause the second phase to trigger. This is the fastest method; you can also perform this skip by exploding a bomb next to the blowhole as well.
There are several small timesavers for the second phase of the Bilocyte fight.
At the beginning of the third Imprisoned fight, it's possible to use the first vent to get to the upper ledge. Fire the Groosenator (with cancelling) as its third step lands (or about 4.1 seconds after the fight starts). If the timing was right, the first vent should be active between the Imprisoned's arms, and carry you to the upper ledge where you can then jump on its head for the first strike.
This trick saves about 5 seconds, but if you miss it costs 30-40 seconds. The window for the shot is somewhat precise.
The general strategy for this fight is as follows:
Alternatively, if you don't want to try the quick shot, take the second vent up and use the Groosenator to stun the Imprisoned, then jump on its head and get the first hit in.
Hug the left wall and roll into this barrier cutscene; this will spawn the Bokoblin leaders away from the horde following you. Do straight slashes on the one that spawns behind you, then turn and do straight slashes on the other four. Once they are dead, use a Skyward Strike to kill most of the regular Bokoblins; this will help set up the next barrier.
The last group of Bokoblins that spawns before this barrier should have two rows of Bokoblins in columns; you want to enter this barrier cutscene by running between the second and third columns from the left, as close to the Bokoblins on your left as you can get. When the Moblins spawn, one should be in the back-left corner.
Hold the control stick up and left as the cutscene ends, then flick it halfway towards straight up after half a second. If done correctly, you'll run up the Moblin's shield at an angle, leaping over the fence and landing on the lower tier.
This trick skips the obnoxious Blue Bokoblin at the third barrier completely, and skips killing the Moblins at the second barrier, saving about 40 seconds and making the fight much easier.
If you miss the jump over the fence, stay in the back corner until the Bokoblin's bombs explode. This will often (but not always) kill all three Moblins, allowing you to continue right away.
The Blue Bokoblin here can take a ton of damage before falling, but will die instantly if you knock him over the inner fence.
Enter this barrier cutscene hugging the left wall. When the cutscene ends, do one horizontal spin attack, then a second to clear space around you. When the Blue Bokoblin charges you, a third horizontal spin attack should knock him over the edge.
If the quick kill fails, just try to lure the Blue Bokoblin to the inner fence and knock him over the fence with a horizontal spin attack.
The positioning for this barrier cutscene doesn't really matter. Each Stalfos will take three strikes from the True Master Sword; just try to aim for their openings. Spin attacks are recommended to help clear out the Bokoblins that will be swarming you.
For the fight at the bottom of the spiral, start by charging a Skyward Strike and swinging horizontally. This will clear a large swath of the Bokoblins, and you can repeat this once or switch to spin attacks. Once there are just a couple stragglers left, a single strike from the True Master Sword will finish them, so just hunt them down.
For the first part, he will likely try to punch you right away. You can knock him back by shield bashing this attack; then continually slash to knock him back off the edge. As he falls off the edge, doing a front hop will land you next to him, making the ensuing final blow quicker.
For the second two parts, when Ghirahim gets too close to the edge he will block certain directions, so be a little careful with your slashes at the edge. If you can lure him into an attack before he gets to that point, you can shield bash him backwards and skip some of this section. As before, do a front hop off the edge as he falls to get a quicker final blow.
Start by charging a Skyward Strike; stay as far from Ghirahim as you can without him walking forward to close distance. When he attacks, shield bash the attack and stab; the Skyward Strike should hit and stun him, allowing you to get six stabs in before he jumps back.
If he charges his red skyward strike attack, you can knock it back into him immediately if you guess the right way to swing (vertical or horizontal). If he does a dart attack or starts walking towards you, do two right-to-left spin attacks to knock the sword out of his hand and stab him again.
Stay close to Ghirahim and he'll attack you. Shield bash, then immediately do a right-to-left spin attack. This will start to chip away at his sword and he'll reorient it; do a second spin attack in the right direction to destroy the sword, then stab him once. Repeat this process once to defeat him.
This phase is the same as with a shield, with the exception of backflipping to dodge his punches instead of shield bashing.
Use two right-to-left spin attacks to knock the sword out of his hand, then stab him three times. Repeat this twice or use his own red skyward strike to stun him to finish the phase.
Take a step back while charging a Skyward Strike and immediately shoot it vertically. Ghirahim will block, and you can then destroy his sword and stab him. Repeat once to defeat Ghirahim.
Do the following sword slashes:
Using a shield is a more consistent method of fighting than shieldless, but it is slower by a few seconds over the optimal shieldless strategy.
Do the following sword slashes.
This is actually the fastest strategy out of all of them, but is difficult to get fully consistent. An alternate shieldless strategy for this phase that is slightly more consistent:
This is the fastest way to kill him in phase two without a shield; alternatively, you can start the fight by closing distance immediately, dodging an attack with a backflip, and then attacking as he starts his lightning strike attack.