Me and platformers dont get along to be honest, but I like the visual style the game has going for it!
Only got to level with the boxes you teleport to with the sword mixed with saw-blades.
I ran into a glitch on the level that introduces sliding. When I got to the end jumping just made me jump instead of taking me to the next level. I tried the level again and it worked. Sorry no idea what I did different the second time.
Also if my back is against the wall the sword if its sent out will hit the wall and just come back to me. Might be better worth considering giving it a half sec of no collision detection to avoid that.
Good luck with the game!