This game looked like so much fun that I gave it a try myself. I TASed the first level, and found a few tricks that you might find useful:
1. When attacking on ground, you normally stop for a few frames. If you press down+A when $00E4 and $00E2 both are 1, you can avoid some of this stop (this trick saves 2f each time its pulled off).
2.Our hero moves very slow in mid-air, so all jumps should be kept as low as possible.
3.Using a vine on the platform, like IvanovishGC does in his youtube video, is faster than jumping over it normally.
4.You can cancel sliding by performing an attack, which allows you to perform slides on tight spaces. This should be combined with trick 1, to lose as little time as possible.
Here is the .fm2 I have of the first level. It's 170 frames faster than your run now (4f from the start menu), and it might be possible to improve it a bit further. With all these things in mind, I think a lot of more frames can be shaved off from your current WIP.
I hope that this encourages you, and doesn't discourage you, to redo your run. I know it can be a pain having to redo something, but you will almost surely learn a lot in the process. I think this is qiute a good game choise, and an optimized run will be pretty fast. I'm looking forward to your progress!
