Create combos whenever possible. The more matches you make, the more moves you will get. You will need at least three matches for one extra move. If no combos are available, make the longest pair, but also consider your stats.
General strategy
Strategize your moves carefully. You can see your balls and switch between the ones that you are shooting. Different colors will cause different effects on the level. Use choices that will result in the largest possible combo for extra moves. You can also view the balls your opponent can use, and decide which matches will work the best against them.
Layout
When levels place balls where one end is unreachable from your side and the other is unreachable from your opponent's side, work on building up your side first. Then, sabotage your enemy with the extra balls.
Sabotaging
Break sets of two balls when you have no match to make. The less matches your opponent makes, the faster you will win.
Upgrades
Upgrades can be purchased with your level rewards. Get Red Balls first for extra damage. Afterwards, purchase Blue Balls to increase your shield and minimize damage. Next, purchase either one upgrade to your Health Balls or Purple Balls. Finally, upgrade Green Balls. When given a choice, always choose to increase your damage.