Good idea, a bit too challenging to be fun.
I like what you have here, it would seem to be a fun game, but there's too much that needs improvement. For starters the weapon system is way to slow and 'unresponsive'. I could sit firing at an enemy for a good minute without a single shot registering, the bullets seem to slow to make this kinda of scheme work.
Also there's the problem of a boss on one of the beginning levels. I found myself swarmed with enemies and not enough powerups to defend myself, plus i couldn't go back to the shop to buy upgrades once I got to that point.
All in all this is a fun game and I hope you take some of these suggestions (mine and others) and release and updated version. I'd look forward to trying again later.