Interesting idea of non combat boss fights, but that also leads to many flaws. First of all it feels largely un-interactive gameplay, like you literally can't do anything to progress faster. This feels even worse on the second boss where you can almost stand still for the entire fight, only moving when the bow appears. Maybe some sort of side objectives like puzzles or something to "weaken" the boss could be a nice way to add interactivity without combat.
On the other hand you could've tried making it more of a rhythm bullet hell game, considering the set time for each boss fight, so the way to react to everything would be more music based and could feel a lot more interactive. It would still be reactive gameplay, but a larger emphasis on music could perhaps work.