no you dont need final island all you need to do is have the music box and never use it it just stays in your toolbox or else if you use it you lose your chances of getting mew you just need to have the music box be above floor 36 and then you just find mew any floor anywhere thats it ok but you need final island to catch one i said one so you can have an army of mew mwahaha
hey you stuck in pokemon mystery dungeon well you come to the right guy you trust me you get free in a dungeon always rely on mad go-getters