So I used to play this game a lot as a kid and I was surprised to see on the leaderboard no one really using it. I could see some people used a bat to punch their way up to the corner of the screen but it got me interested, I used to be able to do it so easily as a kid.
So I downloaded an emulator and think I now remember how I did it. My controller was broken, and the way I could move the dpad meant I could press left and right at the same time. Meaning, if I climbed the vine, pressed left + right as I jumped, then held right I could do this to the underwater doors:
Now I am not sure if this is just on the emulator I am using (OpenEMU on Mac) and if confirmed I am also not sure if it would be an allowed glitch, as I did it as a kid with a broken controller.
Might be of some interest to someone if they are bored, or maybe a TAS run. Bordem brought me this far...