Proper lag reduction at the start of the level will save about 3-4 lag frames, or two real-time frames. The inputs are C-Right, then Mariocam C-Down & C-Left.
The Tip Top of the Huge Island is the second star of Tiny-Huge Island.
Camera setup by Mitagi that gives you the correct angle for the left side triple jump movement. The inputs are: C-Left & C-Down, then Mariocam C-Right & C-Down, and then one more C-Right. Finally, press R after you triple jump.
By pressing Z on the first frame Mario is able to walk after clipping up to the top of the mountain, you are able to preserve your speed, saving half a second or more. The speedkick double-jump ending movement can be done whether or not you preserve speed, but if you don't preserve speed then a dive rollout over the edge of the mountain can be just as fast, but it will be harder to do optimally.