Hi! Thanks so much for playing :)
As far as I know, this is a bug that sometimes happens in the console version. Since it’s an emulation of the Game Boy game, occasionally it doesn’t correctly interpret the code that registers you’ve obtained the character.
The best solution is to have a saved game or a save state from before the battle and replay it. So if you still have your save from the second playthrough, you can try again from there.
Sorry for the inconvenience >_<