Smash through breakable objects in battle maps then run into the Dragon Balls to get them. You must also win the battle.

A more difficult way to get Dragon Balls is to fight somebody in either the Namek or Mountain Road level in Story mode. The Namek level contains a lot of breakables but are difficult to find, especially when you are locked on and your opponent moving and changing your view. The Mountain Road level has almost nothing but trees. If you happen to find Dragon Balls in those levels by accident, pick them up.