So first off let me say the animation and aesthetic here can go places. I do like the thought behind this game with the big lovable but really aggressive character.
What I would suggest, however, is to just really drop the platforming entirely. I think this is a big guy but here he's got a big floaty jump on small platforms, and though I never died in the platforming, I didn't like doing it either.
What I would've loved to see is something like you go up to the bear and it you can really start pounding on it, maybe give it a bit of a minigame, just big juicy punches, if you wanna go overboard finish it off with a throw or some other crazy thing. There's so much potential with these animations, it's just not realized by the mechanics of the gameplay.