Great title screen, nice boss fight and I'm really happy that you had weapon upgrades. I got the reference at the end, haha!
The only feedback I'd give is that the game could be a little bit faster and there could be a bit more visual feedback for the hits (I know how jams go, though, it's crazy), but other than that, it was a really fun game, with a funny, unusual story. And it had a nice number of levels for a game jam. Great job!