It looks great and was fun to play. There are a few things that I am curious about. Did you intend for the ability to climb walls? It added an interesting new way to explore the levels. But, it also made jumping when close to an edge difficult.
Also, I found I could just walk or jump on enemies and kill them if my sword was pointed in their direction - I didn't have to swing (or at least that is what it seemed like). Did you chose to have the sword "armed" at all times?
Your pixel art is awesome btw.