Me vs. You is an achievement in Plants vs. Zombies Heroes. To obtain it, the player must win a multiplayer game.
Simply keep playing multiplayer, and you will likely win a game eventually. If you feel that Ranked is too difficult, you can actually accomplish this via means of playing in Casual. You'll want to bring a good deck with good strategies with you, and perhaps a little bit of good luck. With those, you should be able to succeed.
A slightly sneaky way to obtain this is to stage a game with a friend via the friend system, where they deliberately allow you to win. This will still grant the achievement.