The characters just seem very basic looking. I think they're a good base, but if you added some shading or accents to the characters the graphics would immediately improve.
The thing you described about the enemy attacks is exactly what I mean. I feel like it should either only hit you if you're standing on the tile at the end of your beat or the the beginning of your beat, not both, but I see why you did it that way, and the whole game would have to be designed differently if you did one or the other instead of both. You had some clever ideas here.