This is a nice little cat platformer! I booted up the game solely because of the cats, not gonna lie. But the game does look fabulous! The art is good, the cat is cute, love the levels and the harsh time limit too. I would also like to praise the fact that there are in-level tutorials and that is a very good thing indeed! Good job on that!
The main issue for me is that the controls are a bit unconventional. I do get used to the controls eventually and was having a blast, but its really difficult to understand especially when you just started the game. From my understanding, it seems to be "jump towards the wall with an upward momentum -> wait a bit to trigger the climbing animation -> release and press jump -> quickly change direction if needed" and I've struggled a lot at the first two steps. Not sure how can you fix this without breaking the climbing mechanics, but I'd suggest removing the upward momentum requirement. It may work I don't know.
Anyway, this is quite a nice entry! Well done!