I think it's a very creative and unique idea for the use of the theme to be the cat getting revenge, with the rabbit king's previous actions having a cost, instead of a cost from the players actions!!! not seen anything like that here yet!
The sprites are very cute, the controls are fairly good, and I like that you have included camera shake for feedback from firing the gun, that's good. although I would've liked some continuous firing of bullets, maybe another weapon pick up? : ) also the camera seems to be shaking sometimes when you're just walking around, which I wouldn't recommend keeping as it's bit disorienting imo.
the difficulty scaling from room to room is solid, However I figured out if i got lucky i could just run from room to room without taking any damage, so I would suggest having a variety of enemies, like one's with ranged attacks or at least some stood at the exit of the room. I was also a little bit confused at first when I got to the king because I thought I was going to need to fight him lol, maybe that's a future boss idea to include?
I think it would also be helpful to include items like healing, increasing attack etc.
Overall pretty decent game though, good job!