Really, really lovely game you've made. The animations and enemies are wonderful, simple yet effective, and the game physics feel really really nice, probably my favorite feeling physics from the games I've played through so far. The wall jump is done perfectly so it's not at all clunky or hard to understand.
I actually didn't feel too much of a difficulty spike, I think everything was fairly even and intuitive to figure out.
In some places the room transitions felt a little weird, most have a glow to indicate that a transition is there but a couple did not and so it was a bit surprising and a little hard to read. It was also just at that size where it was getting a little hard to remember the map, but it wasn't too bad. Any more areas and I think a map or some kind of navigation would have been pretty nice.
Overall, a really solid game!