More Specifically, Contest Battles. If you can off your opponent then, by all means, great. But if you CAN'T don't try. Aim for the points. Your Opponent's points go down when one of three things happens.
1. You Dodge
2. You disrupt an opponent's attack
3. You Hit the opponent.
You have a maximum amount of 120 points. Why 120? Points go down by 15. So what's the math?
120/15=8. Yeah, you have to off your opponent's points 8 times to win. Lucky you. You win, obviously, by offing the opponent's pokemon or their points.