I like the simple approach to the theme and limitation. A good excuse to make a fun little platformer. It's been said in comments, but if you'd tweaked some of the jumps by just a tile, then those early challenges would be easier to accomplish and encourage players to keep pushing forward.
I liked the minimalistic art style for the character, but I thought it was odd you mixed pixel sizes. It would have looked more cohesive if you'd designed all the elements with that same chunky pixel look instead of mixing it up for the bat and ground/cliff tiles.
Overall, a great entry for your first jam. You should be proud!