I'm going to be honest that I expected the worst with the MS-Paint style screenshots. The guy kind of reminds me of salad fingers for some reason. But after playing through the demo I was pleasantly surprised, I'd say that the fundamentals are here, you just need to take some time to polish them up!
The movement- right now it's pretty slow and floaty, but the collision detection and platforming (especially the ledge climbing) all work, and it would probably be easy to increase the speed and tightness of the timing (eg. if you ran, jumped, fell, etc. at 200% speed I think it would be much better). As kinoplex mentioned, the wall jumping needs work because it's easy to mess up. Maybe if you "stick" to the wall for a few frames without sliding down, then players could take their time to line up the next leap.
Basically you have the core components of a platformer ready to go, and the question is what will you add next? Enemies? Objectives? You can take it in any direction from here. Maybe just have someone help you with the art :P (the music is max comfy though!)