You have a good idea for a game, but it lacks a lot of polish.
It is very buggy, and a lot of the art and sounds don't go well together. I don't want to insult you or anything but the character looks like he was made with MS paint and he doesn't seem to go with the tileset the game has.
I was kind of surprised that the game had a cutscene with a phoenix, but the game lacked a story and I half expected something to happen at the end.
I have played another game in the jam similar to this called Equivalence where death is necessary to progress, but I don't think it works for this game, (it didn't really work for Equivalence either) it feels more like an afterthought to fit the jams theme. Does it work to kill your self to get further, or is it just better to hit a button and teleport where your sword is? These are things you have to think about.
You get a lot of points for simplicity, but the checkpoints are invisible and at first I didn't realize they gave you more rings. I would just get rid of the ring mechanic and make it an unlimited amount of uses.
For the future all I have to say is give yourself more opportunity to tighten everything together and make it feel good to play.