Nice WIP, Glitchman. I really like what you did with slippery surface momentum in Buffalo's stage and the saber in Doppler 2 and the boss rush.
If you are looking to redo it, there are only a few things that stood out to me as potential improvements:
1. I'm pretty sure you can save a frame grabbing a ladder to go down if it's possible to precede it with a full-length dash. It looks you did this on some ladders where it was possible, but not the first one on the intro stage for instance.
2. I recall the last part of the first climb in Catfish being faster without any doublekicks rather than with.
3. I'm not sure if this will save time in any%(maybe a few frames), but you can make Hornet continue to move to the left side of the room at the start of the fight to hit him earier. I'm not sure how that will play out in regards to ending the fight with him at a low position though; maybe you already tested this.
4. I think it's possible to jump 2 frames earlier and kill the last enemy before the spikeball section in Doppler 1 with Triad Thunder to go over the ledge at a higher velocity.
5. For Mosquitus, I had an idea of a strat that would go something like calling Zero earlier so you can use your first green shot before the door, shoot the 2nd shot at Mosquitus while you're jumping into him and let him grab you, then bait him over to the right as you're sabering him. I don't know if it would be faster than what you did, but it might be worth testing. Also the RNG on his descent after the fight can be improved if you make him fly either towards Zero or down+right every 4 frames; that would require some dissasembly to manipulate though.
6. You can hit Dr. Doppler earlier at the start of the fight if you don't trigger the regeneration shield. This is assuming its possible to dodge his first shot from that pattern though and I'm not sure if it is. I think the best way to setup that strategy would be to kill the green guy with buster and turnaround kick up the wall so you can waste your preliminary charged shot before the door.
7. There might be more that can be done to reduce lag in the Sigma Virus climb, although it is pretty difficult to reduce lag there without air dash.
In regards to the turnaround kick, it opens some extra possibilities for single wall climbs. This
table shows the average vertical speeds for each walljump interval. Over long vertical distances, the fastest way to climb a single wall is to alternate between a normal kick and a turnaround kick every other jump, and to walljump 13f after each turnaround kick and 23f after each normal kick(strictly because it takes 23f to get close enough to the wall again after a normal walljump). If you have the saber or another wall close by, then it is more optimal to jump 20f after each normal kick if you can put a saber jump or a jump off another wall in between(see the Sigma 4 climb in Nrg_zam's X1 any% run for an example).