The menu looks good, cool background and music.
The ingame music could be spiced up a bit, it sounds like the same 4 tones and they get a bit repetitive.
One problem I have is, when I jump the camera moves very tightly with the character, so I can't see the ground (that is on the original window size), but when I go full size window, I can see outside the playable area.
The textures could have more variation.
I like the character sprite and the theme is consistent.
The colors as a whole could be improved, the character color is a bit bland, pretty sure he would pop out more deservingly with a better color!
The bat's head isnt moving but the body is, when making an animation its generally good to have every part move a little, otherwise it doesn't look good.
Consider adding "Coyote Jump" on your next platformer. It improves the gameplay a lot!
Overall it is a working game and I feel like the colours and some other small things hold it down.
Good job and keep making games!