Possibly missable, but unlikely? You need to play this game within a game long enough to get to a certain place in it and activate an easter egg. This is part of the story, and it might be that you must get the highscore to get that there.
Either way, it's so easy you'll probably get this automatically anyway. Just jump over the eggs the pirds drop, and make sure to stay alive, and eventually you should beat Megan's highscore and unlock the achievement.
I unlocked this without even trying, just trying to get to that point in Pird Mystery with the easter egg, and quite a bit before I got there.