A few more things: You are using the SNES9X core for the run, which is generally not recommended. In this case, that's also what's causing you to lose time in the intro. I also don't see a reason why a new TAS was created with version 2.9.1 of Bizhawk, which was released over 2½ years ago, compared to the newer 2.11.
That said: I improved the ascent in the first stage by two frames by timing the B presses around corners instead of turboing B, you also delayed the hit on the hyena by three frames.
Two seconds saved on the hyena fight at the end of The Elephant Graveyard. You also delay a bit before you run towards the rock that is breaking afterwards:
https://tasvideos.org/UserFiles/Info/639012168313103224
Like 15 frames faster when going up from the water into the frog in Hakuna Matata. You can avoid the ground splat if you go further and grab the edge of the platform instead, which is a little bit faster. First hit on monkey could easily be done 5 frames faster, 7 frames on second hit and then I stopped.
This feels like a rushed TAS and could save a lot of time with further testing.