This was a nice cute platformer. As I've said numerous times already I'm not a big platformer player, but I did find some of the things this tried to be pretty neat.
The controls were mostly easy to get a handle on after the first couple tries, and felt fairly satisfying to successfully grab onto rock. But I do agree the jumping detection needs work.
The music was nice and relaxing, and I loved the cute little "ow!" the character would squeak out when hurt.
Overall, not a bad little platformer, I only made it partway into the second level since I'm kinda pressed for time, but I liked what I played. Good job!