Awesome game! I loved the combination of walking on the ground and climbing on the walls.
I also love how you took the most INNAPROPRIATE animal for climbing... a bird.
Good sense of humour, I love that kinda stuff! xP
Definitely a really silly and cute story as well!
I have a few issues:
The game is pretty slow and repetetive. Maybe you could've added some falls you CAN'T climb on, so you have to jump over them. This adds some platforming to the mix without killing what made the game original in the first place.
The art is really good, but the stamina bar is 1/4th of a pixel in thickness. That's a shame, since you had the pixel size pretty much down except for that. Just make the stamina bar 1 pixel in thickness, alright? :)
The gameboy aesthetic is really nice, but it feels more like and arcade game than a gameboy game. Not that big of a deal, but I don't think they had SAMPLES for the music instruments back in the gameboy days... xP
Make the music more 8-bit like to complete the atmosphere of the game! :)