I really like the concept you've got going! However, I did feel a bit cheated when some of my shots didn't connect with the enemy while clearly passing through it which definitely sounds like a bug.
Other then that I would suggest making each round just a bit different to spice things up. Maybe have some different guns for each run instead of the health/speed/power upgrades you had now. At some point you could even transition into having to fight 2 last iterations.
Oww. I just now read Coatline's comment and realise it's not a bug but a feature that the enemy was invulnerable. Please communicate things like that clearly to the player! A simple shield bubble or some sfx of bullets bouncing of metal could have made it clear that my shots weren't doing anything.