Cool game! I liked the colors you chose for the whole game, including the enemy, the bullets and the background. The enemy's design is great and the atmoshpere was done correctly. The sounds fit well.
Something like a health bar for the boss could be helpful for knowing if you're actually damaging him. Some games make the enemies shine or change their color. Same applies for the bullets, I didn't notice I was able to destroy them.
The way you implemented the limitation was interesting, but as moving is no really precise in this game it's easier to go slower and hit continuously the boss. The limitation felt more like a literal limitation for the player's mobility.
Did you use BeepBox for the music? I thought that based on the soundfont. If that's the case, you should try using some specific scale, it may help to the different melodies from your song to match better. Try adding more different chords during the song to make it less repetitive. I'm not an expert creating music, but listening and listening my songs and changing notes until I like it it's a strategy that worked for me.
Good job, keep doing great games!