To unlock the King in Virtua Tennis 4, 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.