Exploration Platformer
I like the idea of the player being completely unfamiliar with this dark, scary forest where they have to explore to find acorns. The level is the same across all playthroughs but the player gets more and more familiar with the level as they progress and eventually will fly through sections they once struggled with. One possibility is something like Hollow Knight, where the map changes and new places open up as you go further in the level.
Precision Platformer
A version of the game is more like Celeste, where the player progresses through the game level by level. The player can continually progress their platforming skills with each level. This could also be a puzzle platformer kind of style as well, with each level opening a new mechanic that the player has to figure out how to use to get an acorn.
Fighting Platformer(like Cuphead)
Instead of relying on platforming as a means of movement, it could be really cool to incorporate platforming as a way of fighting. For example, if a squirrel has to fight a fox, it would have to outsmart it by chewing on a branch to make it fall on the fox. Each level could be its own boss like in Cuphead.
