Great scene composition on the intro! I loved the concept very funny idea and character design.
First time I played, before I possessed the sword, I quickly found myself dropping below the parallax zone for the backgrounds. Some ground pinning might be a good idea.
Controls take some getting used to, but aren't unintuitive. I do wonder if maybe controlling the direction of the sword is enough to "lead" the character the same way? Rather than having to swiping the sword in the air to change direction after landing a tight jump?
Great work!