I played a few times and accidentally figured out that you must shoot the powerups to buy them. It worked for me once I did that. That being said, with some additional bosses that have different attack patterns this could have potential.
I would have liked to see some form of health bar to know that I was doing damage to the boss. I know the color changes to represent that, but for the first 10 seconds of shooting, I felt like I was doing no damage to the boss. If you don’t want to put a health bar, then I’d at least add some type of flash animation to the boss or particle effect to the bullets so it’s clear that they are hitting the boss and not just going past.