These are really cool game mechanics, but the difficulty is pretty high right off the bat. There's a lot you have to learn to think about; planning your movement, not hitting the walls, not being hit by projectiles, going after and hitting enemies. It's a bit too much to start off on. The tutorial works great in teaching mechanics, but I think it needs some steps in between the tutorial and the actual game.
How about slowly introducing new hazards? It could start off without the walls killing you; just a quick and simple first level that serves as the tutorial. Next, a more complex level with an enemy that moves around. Next, the enemy shoots projectiles. Next, a level where the walls can kill you. Etc. I'm not sure that fits your theme of a Boss Rush anymore, though.
The controls do feel good and make moving around fun, and the feedback from audio and such feels good as well. The camera movement feels natural too.