I made it to screen six, the one with the staircase full of monsters. The game is overly hard, and at least part of this is due to the controls. If you hit z while running, your character won't stop and shoot. Instead, you have to stop first and then shoot. My first few tries, I couldn't tell I was being damaged--the health indicator doesn't make an eye-catching change. When you hit the top of the enemy, you're frozen until you push them back, and while it doesn't take forever, it does take an awkward, too-long amount of time.
On screen four, there appears to be a higher path you can take, but it doesn't go anywhere. Screen six appears impossible without spending a ton of health, as you cannot jump while shooting. You can jump while running just fine, so I'm not sure if it's a problem with input. I can press a lot of keys before my keyboard ghosts, so if this isn't a gameplay choice there's a problem elsewhere.
The dropdown on screen four, where you can see that the enemy at the bottom of the pit is a shooting enemy before you land, is very well telegraphed, so good on there. Screen three is also pretty well-done, though it would be nice if it was possible to jump under the monster on the second platform. If you can, I couldn't figure it out.
I dig the concept and the flavor of the game--with some gameplay and design tweaks/fixes, I'd gladly give this a higher score. Also, a thumbnail image of any sort would help with first impressions.
The problem is the gameplay and level design, mainly. The art is nice, and meshes well with the sound effects and the music you picked out.