Even showing a life bar for the boss on the screen somewhere would make the players feel some hope as they get more damage done with each attempt. Unfortunately there aren't 200 pixels of width in a Game Boy screen, so you'll need to use multiple bars and give players some despair instead.
Making music for your project is a lot of work, so it's really awesome to learn that all the audio is completely original!
I'll be sure to check out some of your other games if I find some free time after rating all of the jam's entries, I really do love your art.