I figured my notes from reviewing the games might come in handy, so here's what I wrote about your game as I was playing:

Ambitious! I do not understand the teleport dogs at all, they seem super mean! But I did beat it! The shmup at the end was a cute little reward! This could feel so much better with just a few tweaks to the camera, you can’t see where you’re going most of the time, but that’s an easy fix. Nice job.

Just tried this game and managed to beat it after a while. Here are some thoughts and comments:

• Nice platformer! It was fun but controls felt sometimes a bit difficult.
• Good visuals. They are clear and look nice! Cats and dogs division made it easy to understand who your enemies are already the first time seeing them. Similarly spikes and bouncy balls were super clear about their purpose. The background is very aesthetic. Although, there were also some not so clear graphical elements such as the red dots and the blue rectangles. The rectangles were especially confusing because as far as I know they had the same function than the bouncy balls and I kept wondering why they didn't have the same visual. Additionally, I think some objects (like the dog with magic wand and bouncy balls) behaved differently in different places and it felt weird that they shared visuals but in most cases it wasn't super confusing.
• The background music was really enjoyable. I liked how it started as a simple fun music / children song but then evolved to more epic adventure music as the game progressed. As a curiosity, the main melody of the soundtrack reminded me a lot about this song. I guess there are melodic similarities in the beginning of the phrases.
• The upper and lower part of the game are little bit cut off. You could try changing the height value of  itch.io page Viewport dimensions setting. Because of this I didn't notice there was health indicator on the upper left corner and it was very confusing to not know when game over would happen. 
• The tutorial text were really nice. Like "Let's go cat!" at the start was somehow motivating.
• The game had appropriate length for a jam game. The levels were interesting but there was a lot of difficulty and length variation between them. For example the first level was really difficult compared to the second level which was (If I remember correctly) a lot shorter than all the other levels. That last level with flying clouds was fun because it changed the gameplay but I think it also was a bit difficult.
• In my opinion the spawning dog was quite annoying. I suppose it was supposed to be difficult but I felt that there was no real chance to escape from it because they can just spawn in front of you (or in worst case on top of you!) and the player character is not much faster than the enemies so escaping was super difficult. I felt that I always managed to escape only by random chance and not because of my skills.

Overall this was a nice jam platformer. It was fun to try it.

If any of you have a chance to try either of the games I participated creating (DNA & Travelling Neighbors), please consider leaving at least some feedback for it. Positive or constructive are both welcome and greatly appreciated.