Howdy! I recently picked up this game for RTA runs and found some stuff that might help improve the TAS.
Regarding getting the Level 2 Wind ring, I sometimes find that the Ice Dagger projectile kills a sand worm right as the worm spawns. I think it's either hitting all the body segments at once or finding some way to bounce back and forth on the edge of a slope to hit the worm repeatedly. IIRC, the second worm is the one I've seen this the most frequently. This should be faster than killing the turret enemy to get the wind ring. I haven't been able to get this consistently RTA, but that shouldn't be an issue in a TAS environment.
I was doing some testing on the Stage 4 boss, and found that the Fire Viper (Level 3 Fire + Level 1 Earth) seems to deal more damage than the Wave attack (standing under the boss's head and aiming up). What's very strange about this is that if I put Fire Viper on the left hand, it consistently hits the boss then has extra segments of the attack that I have to wait forever for. However, if I put Fire Viper on the right hand, it consistently hits the boss and has no leftover body segments and I can spam the attack much more quickly. Probably the optimal strategy would be to put Wave on the left hand earlier and add Fire Viper to the right hand when the fight starts in order to use both for the boss. Obviously, even if it does save time it would have to make up for the extra menuing, which should be slightly offset by Fire Viper being closer to the Blade for the Bone Dragon fight.
Relatedly, I think left hand vs right hand might make a difference vs the Stage 3 boss. With the rings on the right hand I can spam the attack constantly while the TAS looks like it has little gaps in the attack animation on the left hand.
Edit: Also, have you considered Wall of Flame against the Stage 2 skeleton miniboss? I realize that imposes menu costs but it should allow you to hit a lot of his pieces simultaneously
Edit 2:
Here are some videos demonstrating left-hand vs right-hand differences on the Stage 3 and 4 bosses:
Stage 3 boss:
https://youtu.be/L-782KTDBL4
https://youtu.be/IbzoVmR4clc
https://youtu.be/bHYpTXLdbG0
https://youtu.be/ivdDEsqfy8c
Stage 4 boss:
https://youtu.be/Ol1lIXtHAkU
https://youtu.be/gnx9V6-TjMo
https://youtu.be/qCtUF8Zw0XY
https://youtu.be/NcUbQ8vDdx8