The concept is really cool, I absolutely loved how the cowboy vibe was conveyed in the game, both in the art and sound design (the music in special fit very well for that atmosphere). I think it just needs a lot more polishing on the gameplay itself.
The controllers felt decent at first but quite janky or inconsistent with some upgrades and sometimes when grabbing edges. Took me a long time to figure out how to do the wall jumping, which is definitely not obvious as you have to face away from the wall before jumping again (from my understanding).
The 2.5D visuals are great but being able to move in depth instead of just left and right felt a bit weird at times, mainly accounting for the fact you are limited to left and right when grabbing edges, shooting, rolling, etc. The bear in special was kind of annoying only because of that.
I like the idea of the bird's attack, but I think the reaction time is a little too tight. I feel it should be a bit slower and/or have some kind of visible warning on the bird to communicate it's about to happen, this way relying more on the player's timing rather than purely reaction time.
(also, because of that, one of the last birds in those platforms just feels REALLY merciless imo as it attacks as you're about to reach a very small platform, easily taking you down and killing you from fall damage).
For the map itself, there were some areas where collision was just very inconsistent. Worth to mention the secret place on that river on the beginning, which got me falling down below the ground infinitely to the limbo with no way of coming back but restarting the game.
Overall, I did have some fun and I do think there's a lot of potential in this. I'm also interested in checking it out again later in case you keep working on it post-jam. Nice entry!