Neat game concept. I don't usually care much for action platformers, but looks and plays better than I initially thought it would. It's clear you put a lot of time and thought into this.
Time for the bad news. I do not know if these are intentional, so feel free to call me out if I'm wrong.
1. The cooldown for air shuriken is inconsistent with ground shuriken. Air shuriken cooldown lasts only as long as a shuriken is on screen. The instant a shuriken disappears from hitting an enemy or wall, Azumi can immediately throw another one. Also, air shuriken do not cost meter.
2. Similar to shuriken, ground and air sword slashes are also inconsistent. The first 3 strikes of the ground sword combo cancel into each other, so the slashes will come out as fast as you press them. This makes killing the larger enemies too easy because you can mash them to death very quickly in a way that feels unintentional.
3. Attacking or dashing while holding the jump button will make Azumi immediately perform her double jump. This is a slight problem because of jump height being determined by how long you hold the button down, as well as air attacks killing your upward momentum.
4. Too much screen shake. It's a disorienting when both landed attacked and enemy deaths cause different amounts of screen shake in the middle of a fight, especially when being swarmed by enemies. Personally, it also has an unintended effect of making Azumi momentarily blend in with the background because of their similar color hues. I think this could be solved by giving Azumi a visible outline like in her concept art, but that's a more of a suggestion than a bug.
Aaaand that's it.
I look forward to playing the next update of the game!