Unlocking the King is not easy and it has only recently become clear how to do it. Beating the King is required for the Great King Trophy.
To unlock King, you need to win every game in Arcade mode without dropping a game or going to deuce at any stage. Not only that, but you need to get a medal on 5 out of the 6 medal categories. This means you need an ace or dropshot to qualify.
You will then be treated to a match against King. Beat him to unlock him.
He is a tough opponent, and you should aim for his forehand.
Note: choose retry if you fail, otherwise you need to play through Arcade mode again to get the game back! This can be done on any difficulty setting.