Wow, this one really blew me away. Great use of the theme and great design all around!
The boss fight was a really neat idea, but kinda rubbed me the wrong way in the sense that I couldn't really gain a sense of progress as much as I did during the first part of the game. There were points where the cat's tongue stopped flashing, but he still attacked a few more times before moving to the next phase...is that supposed to happen? I feel like he should back off once I've drained his "HP".
I gave it a good couple of tries, but ultimately I gave up on the leg part. I might have been a little more inclined to stick with it if there was a way to dodge if I picked the wrong side during the sweeps (or at least a better cue on which side to go), but I couldn't get it down well enough to get past it (and the one time I did, I got stomped on...which feels a little unfair since pushing too close to the edge means I die as well). I also struggled with the jumping issue that others had mentioned, which contributed to my death a few times.
Anyway, cat boss gripes aside, this is easily my favorite entry thus far and I'd love to see a little more polish on it. Great work!