This is beautiful and very well done. The sound design does a good job communicating and the game looks really great. The level design seems very interesting, and should showcase the advanced movement methods if I can ever get there. :P
The light effects and general art implementation and asset quality is fantastic. Well beyond expected Jam quality.
The background music does a great job setting the tone and situation.
The sound effects help immerse and frame the interactions well.
The story carries into the game sufficiently, but of course in a more full incarnation it should be set up in-game.
General improvements feedback:
* The player spends a long time winding up to hit, the hit timing is short, and there's a window of cooldown. Works well in a fighting game, but in a platformer it's a long commitment and planning time with a very short reach.
* It's unclear when a hit enemy will be stunned or killed
* Enemies seem to do variable amounts of damage, with no indication for why
* A stunned enemy probably shouldn't hurt to walk into
* I couldn't seem to jump over the tall enemies, so even stunned they would often kill me
* You might be interested in the concept of "coyote time"; jumping right after having left a ledge
* Given the non-linear nature, a map would be very useful
* The jump is very much a commitment, and I feel very floaty during it.
* You could set up platforms with one way collisions, and the visuals for platforms should better communicate solid barriers. One technique for this is all solid barriers have a specific color outline.