By jumping off the platform with the key in the first room and doing a precise jumpslash afterwards you can skip talking to the old mogma and can go directly to the next room.
In the first lava river room after the Dark Lizalfos, it is possible to skip flying the Hook Beetle to grab a bomb flower, by instead placing your own bomb and using precise Hook Beetle flying to reach the rocks blocking the lava spout, destroying them.
This trick is fairly precise; you need the Beetle to be flying upward as little as possible while still clearing the fence, and the bomb needs to be placed as close to the fence as possible while still allowing the Hook Beetle to clear it.
In the two level room with the water plants and frog statue, it is possible to avoid going to the second level. Get a water plant on your sword, run to the area below the frog statue, and do a front hop jumpslash. The water plant should shatter on the frog statue, triggering it and lowering the fire wall.
When you fight the two Magmanos before the Mogma Mitts, there is a consistent strategy to kill both with a single water plant. At the beginning of the fight, run straight across the room to the platform and grab the water plant at the top. Then drop down and stand next to the platform. Right before the Magmanos attack, take a couple steps backwards towards the wall. One Magmanos should raise the platform while the second should emerge right next to the first. You can then hit both with the water plant and destroy them with spin attacks.
After defeating the Magmanos, there is typically a cutscene where the hanging Mogma congratulates you on your victory and asks you to get him down. This cutscene can be skipped by calling Fi as the fight ends; the timing is lenient. If the skip works, you will see the lava in the room lower while you are speaking to Fi.
Which Fi textbox you get affects how much time you will save; Fi's low battery message trumps all others, and is actually the best (or tied for the best) option. Fi's standard message is the next best option, and last is Fi's low on hearts message. For the last, you have a chance of getting Heart Dowsing, which would end up losing time to the cutscene (though this seems to occur rarely, if ever).
After obtaining the Mogma Mitts, deathwarp to the first statue and save. Activate BiT and BiTWarp using the Upper Academy statue. The room you end up in will be partially loaded, and you must reach the door across the broken bridge to reload it.
To reach the other side, first do a manual jump to get on the right wall. To get around the pillar, you will do a forward jump followed by a jump slash. This angle is precise. To get the correct angle, while holding Z, slowly angle the control stick until Link's feet are in-place walking forward, and Link should not be drifting to the left at all. Because of the round shape of the pillar, the forward jump will push Link to the right and the jump slash will bring him back to the left.
Once on the other side, go through the door into a completely unloaded room, and then return back through the door again. The bridge room will now be fully loaded; move to the left side of the bridge and jump down to the passageway in the statue's mouth. From there you can play through normally to the Boss Key.
After the BiTWarp, instead of reloading via the opposite door, you can reload with the door behind you. The fastest method is to carefully position yourself while executing the BiTWarp in Skyloft; with the correct positioning, you'll fall through the upper platform and land on the door sill, allowing you to immediately open the door. You then still must do the pillar jump above to get across the gap, but you can immediately jump to the shining platform after that.
In general, the Moldorm fight is fairly random; he will turn and pause in random places. There's a best fight that should be strived for:
If Moldorm turns the wrong way during the above strategy, he'll be right on top of you. Try to back away and hope he turns off, allowing you to get the second hit in.
If that goes wrong, the general strategy is to never chase Moldorm. Let him come to you, and try to bait attacks and dodge them. In his last phase, Moldorm will charge you and charge in a straight line until he hits a wall and is stunned. If you can bait him and dodge him, that should give you enough time to defeat him.
The strategy here is the same as in the first Ghirahim fight, but can be done in three cycles as follows:
Using a vertical spin attack for the last one causes him to backflip to the second phase faster.
Ghirahim has multiple attacks during this phase, and he attacks in an unpredictable pattern.
Ghirahim will attack you with both swords without warning. You can shield bash and do a horizontal slash to cancel it. This won't damage him, but it is faster than backflipping to dodge. He will sometimes continue into the Leaping Strike.
Ghirahim will do nothing at first but suddenly attacks without warning. He is vulnerable right before attacking, so if you can recognize this attack coming you can preempt his attack.
Ghirahim will walk towards you while blocking in two directions. This is the best attack to get, as you can immediately attack his open area and get in a few slashes. In this attack, his stun length is always short, so five slashes is the most you can get (see below).
Ghirahim will walk towards you while licking his sword. He will block your first two attacks, but then he is vulnerable. One method to deal with this attack is:
Ghirahim will summon a horizontal circle or vertical semicircle of darts around you. Do the appropriate spin attack to send all the darts flying back at him; this does a small amount of damage. While it seems like you can hit him while he summons the darts, this doesn't actually do any damage.
Ghirahim will summon a circle of darts around himself and fire them at you in three sets of five. There are two ways to deal with this attack. The first method is to slash each set of five as it appears to cancel the attack; this does not leave Ghirahim vulnerable and is slow. The second way is to get close to Ghirahim and keep doing horizontal slashes. This will sometimes cause him to transition into a Leaping Strike. If you hit him after that attack it will despawn Ghirahim's darts.
Similar to the Dart Circle, it seems like you can hit him when he summons these darts, but it actually doesn't deal any damage.
Ghirahim will leap into the air, and after a second or two land with both swords down where you are standing. After he lands, he is vulnerable while he pulls his swords out of the ground. You can dodge this attack by just backflipping once while he is in midair, then slashing him as he recovers.
It is NOT possible to stunlock Ghirahim; this is false information. Instead, his stun length varies with his health and whether or not he used Imminent Attack. The Imminent Attack always sets the stun length to its shortest, at 5 hits maximum. For any other attack (Feint Attack, Sword Lick, or Leaping Strike), if he has most of his HP left, the stun length is longer (around 8 slashes or so). Once his HP is lower (around 2/3 HP left), the stun length is always short. So the only time the longer stun length occurs is if he uses Feint Attack, Sword Lick, or Leaping Strike in the first or second cycles.
At the start of the Fire Sanctuary, it is possible to skip the cutscene showing the waterplant falling into and solidifying the lava by talking to the bird statue at the same time the cutscene would occur.
This strat is probably slower in an RTA format, but may be slightly faster for a TAS.
This method is slower than playing this section normally.
Save at the bird statue when you reach the first outdoor area. Activate BiT and BiTWarp using the Lower Academy statue. Link will appear in a partially loaded room; to reload, exit through the door on the left.
You'll need to defeat the Dark Lizalfos; however, since you haven't triggered the Dark Lizalfos cutscene, he is stuck in a wait state. If you try to hit him then he will keep teleporting back to his initial state, making him invincible. To kill him, stun him with the Gust Bellows or the Whip, then use a spin attack and final blow. Then continue through the door that opened.