Yay, my first japanese TAS. HOWEVER...this is a WIP, which is why I only play like three levels. No procrastination shall be done here as I did with Kirby Super Star.
Explanations:
Face-Bounce: I call this Face Bounce because the only area you see of Starfy actually making impact is his face. Anyway, on the section with the...uhm...black bubble balloon things, I simply swim on the other side and bump into them to get a quick boost. This sets Starfy's velocity a little higher than when he turbo-swims, but only for a half-second.
Water-Snap: If Starfy is turbo-swimming toward the surface and moves diagonally, there is a split second where you can hit the A button JUST BEFORE jumping out of the water where he will instantly dart forward and out, moving a little faster.
Talk To The Fins: Sometimes scrolling through all the Hiragana/Katekana in this game can be so boring. And it wastes a lot of time. (I'm not sure if you can skip the first conversation with Moe/Kyorosuke at the cave before Herman/Yadokarita, but that's where I found this glitch.) In order to avoid this, whenever dialogue starts, I press the Start button just before the dialogue window starts to lower down and then unpause. This makes a huge difference and saves about three seconds or so, because I'm able to open the door next to Herman without even having to listen to him blab about Old Man Lobber.
Again, this is very WIP.