Very cool aesthetic, I really enjoyed the variety of backgrounds and the feel of the different areas (although space was... weird :P). The movement was very fluid and smooth and the jumping felt precise and controllable. The attack, once I got it, was satisfying and I liked that it was more of a stun than an actual attack, I wasn't incentivized to go around clearing out entire maps of enemies. I liked the abundant health pickups and the jumping puzzles later in the game (well, the devices that you'd have to whack and land on in the same jump). I also cracked up every time my cat got hit, and appreciate that there's a dedicated button to "meow".
Some feedback:
1. The world is big and I don't have a map (as far as I could tell). I eventually got my head wrapped around the central thoroughfare, but the space map was particularly disorienting and took me awhile to work my way through.
2. Similar to the above, I never really felt like I had any guidance, I was just kind of let loose in the world and had to guess where you wanted me to go. There was a fairly natural progression in the beginning of the game up to the first ability, but after that I was sort of just wandering around aimlessly until I found the next one.
3. It was unclear to me what the CDs were for, if they were necessary for progress or just a bonus collectible. I got to the end, so now I know, but having all these items scattered around and me not necessarily knowing where I was supposed to go at the same time just sort of had me worried that I needed to find X CDs and then take them somewhere or something. Probably a me problem, but it was there in the back of my mind.
Anyway, I enjoyed my time with the game. Good implementation, great aesthetic, and a cool usage of the theme. I'm happy I got to help the cat escape cyberspace!