It looks a bit like a 'basic' game, nothing we haven't seen before. I would add under the intro 'Enter to skip' so you don't have to torture the minds of people who forgot you could skip it.
Anyway I played for about 5 mins, I couldn't understand what it was that he's throwing, is it an egg or something? And who or what is that imitation of you? Or is it supposed to be mysterious. I like the music. It's good music for a platformer. Graphics could be improved by adding more/beter detail to the tileblocks, to make it look more like that 80's pixel style if that's what you were after.
Oh and I would respawn the player where, or at least close before where you died. It was already annoying enough to have to do so constant double jumps and quickly having to kill aliens once you're on the platform, and now I have to kill the exact same aliens repeating everything. No one likes having to start over.
By the way, I initially thought you could pick up those alien eyes, I thought they were something to collect, although it was a nice touch that the eye follows you. I would use that 'eye left on the floor' feature for those 'indestructible' aliens, as it's temporarily downed, it would pop back to life after a while.