Graphics
I liked your ostrich and background sprite work. I did find that the colors didn't clearly distinguish the playspace from the background enough (specifically in the opening sections) which made it difficult to process what I was looking at. Nice touch on coloring the sprite when underwater.
Character Controller
I think you've got the perfect amount of acceleration/deceleration while grounded. That's an easy thing to get wrong, but this felt really good. The values still feel off to me on the jump which feels floaty, but since you're going for a Joust kind of a thing, maybe it's fine. I'd like more game feel stuff here. However, since one of your goals is to actually be able to release a GBC/NES version, you're somewhat limited in how to accomplish this. Doinksoft (the indie devs behind Gunbrella and Gato Roboto) showed me you can still do it in GBA by adding sound, impact and death effects, screen shake, and hit flash. (I knew GBA can handle this, but unsure on GBC/NES). Regardless, right now, the attack feels like it does nothing and isn't useful.
Story
The character suddenly appearing on my back made no sense, though I'm sure you're already aware of that. That opening cutscene is a cool idea. Here's some things that I ran into that would help you pull it off better. Due to the small pixel count and comic panel frames moving right to left (which goes against what's intuitive in American information flow [left -> right]), this is confusing to parse what's happening. By the end, I get that there's an explosion, but I had no idea what I was looking at until after it was over. It seems to freeze on the first frame and require a button press to continue, which makes me think the game has crashed. This would probably be clearer if you had the screen flash white / the color of the explosion, then fade down into the scene. While I like the style choice of the comic panels, if you actually want to design this for GBC/NES, I don't know that it will work. The screen/pixel count is so small compared to the amount of information you're trying to squish into it. Full frame would fit your platform of choice better. Either way, keep an eye on this when playtesting with other people if you continue development
Sound
Nice job on the music (and a lot of it!) The world and controls would feel a lot more alive with more sound work.
Level Design
This would be improved with more intentionality about how you introduce challenges. Right now, it feels like enemies are just thrown at you without consideration for teaching how each one works and how to deal with it before mixing and matching to try and create interesting gameplay moments. The little exploration teaser on the right is fun, nice. Expanding the game space as you move downwards is an interesting choice. I think this works as long as you don't try and introduce the enemy at the same time, as reacting to it can feel unfair when it's impossible to see. Especially for an early section of the game where you're still "teaching" the player exploration.
I'd be curious to see where you can get with this in six months!