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.
If missed, a B-hop attack can be used instead. It's possible to dig immediately after landing.
Falling in just the right place near the right side of the tunnel exit makes the cutscene trigger right after Link begins falling, whereas it normally only triggers after Link has reached the ground.
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. When learning where to jump, it can be helpful to use tpgz's switch area trigger viewer.

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 but comes with a high risk of failing and voiding out. If you got the Midna text skip on Castle Rooftops, you will re-spawn in the trigger if you fail this trick, but it is possible to do the jump attack skip again.
See this page.