Did you get the double jump or dash upgrade? the double jump upgrade can be found to the right and up from the drop off, while the dash can be found three rooms to the left and two rooms up from the drop off. While you can theoretically beat all bosses with only the stick and no powerups, you really need either the double jump or the dash else the next few bosses will be of a nightmarish difficulty. Finding a few Inkhearts helps a ton. Only reason why I didn't force the players to get some of those powerups before the boss is because it was designed to be a speedrun type game that allows some progression skips.
Seriously though, not even I can beat that boss without dash, double jump, or with just three hearts... (also if you fall next to it instead of falling directly into it you can dodge its attacks a lot easier)