After the first cutscene, it is possible to break the box blocking the digging hole earlier than intended. This saves 2 frames (approximately 0.07 seconds) compared to breaking the box after the cutscene.
1) Dash after the first cutscene. 2) Immediately dash straight forward. 3) Hold up-left and count Wolf Link's steps up to 6. 4) Right after the 7th step, mash B for 3 attacks. 5) After the third B-attack, hold left and B-attack again.
It is possible to speed up the dialogue with Midna after the crawlspace by using Text Displacement (TD). Right before the cutscene trigger, it is possible to target Midna and speak with her, which results in TD. Doing so once, then entering the cutscene trigger, causes the cutscene to start with the second set of dialogue boxes, ultimately saving approximately 0.5 seconds over triggering the cutscene normally.
After entering the tower staircase, it is possible to skip the Midna text by jumping to the side of the stairs at a specific angle. You should be just to the side of the full collision. Jumping too far to the side will result in skipping the trigger which activates the Midna jump as well, resulting in having to re-try the trick.
Upon entering the Castle Rooftops, there is a 1 frame window to skip the Midna text via a jump attack immediately after the cutscene is skipped.
On the Castle Rooftops, it is possible to make a diagonal jump onto the collision instead of climbing the ledge. This very risky strat saves approximately 0.3 seconds done well, however, comes with a high risk of failing and voiding out. Note that if you got the Midna text skip on Castle Rooftops, you will re-spawn in the trigger if you fail this trick, and will have to do the jump attack skip again.
There is a bulblin archer at the bottom of the tower. It is required* to kill him to proceed up the tower, else he will snipe you down later on.
Spin attack to deflect his arrow, then as he backs away, knock him into the water (which kills him instantly).
Dashing along the inside of the staircase, time a sidehop into the outer wall to dodge the arrow (this is difficult), then as he backs away, knock him into the water (which kills him instantly).
There is actually a method to skip killing the bulblin archer entirely. This is incredibly difficult to do and is not recommended for RTA attempts, but it is shown here for completeness's sake.
Once on the Castle Rooftops, with good movement, it is possible to make an earlier wind cycle than intended. The TAS jump listed above can make this cycle easier to achieve but is very risky. If you do make the cycle, you will have to do a diagonal jump off the bridge to the lower collision in order to avoid voiding out, as the wind dissipates as you reach the bridge. The video below shows this.
If you miss the cycle, it is possible to call Midna to reset the wind cycle and avoid having to wait as long.