Wow, the level design in this one is excellent! All obstacles are used in creative, memorable ways, and I love the systematic, puzzle-like approach to beating a level. The length and variety in each level were just right. The theming, short boss battles and bits of dialogue added a lot to the atmosphere.
The only criticism I have is that the jump physics did not feel as good as they could have been (very little air-time), and the last level was a bit repetitive. Also, maybe consider slightly reducing the complexity of the controls. Other than that, I enjoyed it a lot, it's a very promising concept!