Wow, this has some potential for a big game! I like the simplicity and clarity of what to do and how to do it, although inversion didn't work as I expected at the beginning of the second level and then I got stuck there. But I like the music, sounds, a visual style. Maybe speed up the movement for some quick dashing through the levels. Cool spin on the theme! I think you've done a nice job!
*** Ooh! Gamepad support! NICE! You should really mention that! ***
Now that I've played to ...uh... needs a level counter! Got to something like Level 6. There are parts that are frustrating to fail because it takes a little too much work to get over to them to try again.
I really hope you continue this game because you're on the right track. I'd add check points or make replay of each level less frustrating. Visually, though, I love your level designs. The cavern was one of my favorites. Love the background pieces except when it's hard tell them from the foreground.
Sorry, this is a lot of babble, but I'm a fan and really would love to know that you continue and level up this game. It's a really fun one!