I think this a decent game with mostly good level design that genuinely looks and feels like a Game Boy game.
I just wish the game's platforming physics were a little better and less stiff (unless that was intentional to fit with the old man), while the art direction could have had a bit more love put into it.
I also feel that using the double jump skipped some of the challenges and dying in some levels means you have to do them all over again (but not all of them and I'm glad the key is stored even if you die). There was even one point where I had to make a leap of faith.
Otherwise, keep up the good work and I like the main character.