Emulator: VisualBoyAdvance Emulator Version 1.7.2 re-recording 19.3
This improvement of 69 frames (1.15 seconds) was achieved through corner boosting, putting more thought into where Link should be before entering the next screen, and better manipulation and lag avoidance on the boss.
Tricks and glitches
Screenwarp
This is done by pressing select just before the screen starts changing when moving to another screen. It causes Link to warp to the other side of the screen.
Up/down + A and B
This is done by pressing up and down at the same time, then pressing the A or B button. Pressing A causes Link to become graphically distorted, and can lead to some cool side effects. As you'll see in the boss battle, I turn into Dark Link. Pressing B makes the game think Link is at another part of the screen, which was used to get the sword without actually going down to it.
Corner boosting
This only works on corners which you're moving away from, i.e., it won't work on the corner while exiting the house at the start of the game. It will, however, work on the two corners outside the house, and the one before entering the dungeon. It's done by moving Link into the corner on a certain frame, and it causes him to be pushed forwards a bit. It saves 1 frame each time it's done.
Thanks to...
Soulrivers, for his previous run, and advice on the boss battle.
Tompa, for checking my progress regularly and reporting back any improvable parts.