This definitely needs gamepad controls.
It would be nice if there was some indication how far into a stage you are. Also it's not clear to me if it's a matter of how many enemies you shot down, what score you got, or just how long you managed to keep alive.
I like that there's new game-play elements with each stage (different backgrounds, that move, and new enemies, also the asteroids), but I couldn't make out what new element there might have been on stage 4 (I suppose the time managed to collect a beacon and got a power-up was based on the fact that it was the first time I managed to collect one while not having some damage, so not a new element for stage 4), but there are two new things in stage 3... Also, is it purely random if a healing/power-up beacon appears?
I love the variety of the enemies and their behaviour and different attacks!
How many stages are there in total? I managed to reach stage 4 but not to finish it...
I agree with the other comment about the movement speed. To add some more tactical gameplay, maybe the movement speed could depend on whether you're shooting? So shooting takes some power from the engines and you move slower, if you're not shooting you can move faster?