This was a decently enjoyable demo for me. Is that all that's to the demo? It says three stars available to find, but I was only able to find one.
You should make the jump a bit more fluid or allow some kind of movement in midair. Examples I've cited a lot towards great player control and mobility design are Yoshi's Island and Mega Man X. I should make the note that it's a terrible idea to rob the player of control mid-jump, but specifically going to those points...Yoshi's Island doesn't do that (allowing movement midjump) and differently, Mega Man X allows the player to cancel out of animations at any frame, providing further increased controllability.
I died on the spikes part as for the jump complaint, but that just may be on my own mistake. I just think the jump is kind of stiff, and might not be helpful with later (unfair?) platforming sections.
It was kind of easy to cheese some of the enemies. Is that intentional? Perhaps you can't really fix inherent methods players use to cheese a game (such as if it's just jumping up out of reach to prevent being hit), but it's still worth it to try to endeavor to balance out gameplay.
Have you given enemies a line of sight, or thought about it? You probably have, but I notice they attempt to fire at the player even with a solid block in between them and the player.
A suggestion if you haven't thought about it. Have you thought about adding layered level structures/some sort of vertical depth to levels? I mean like, instead of some levels going on in a left/right direction, have some sections stacked on top of each other, so you can reach the upper portions by jumping into the ceiling gaps seen in the demo.