To get a higher score in a battle, finish the battle with an Overdrive skill. If you finish an enemy off with an Overdrive skill that has a higher level you will get more points in the end. This will only work if the last move in that battle was an overdrive skill. A good way to do this is leave one enemy remaining. Then, lower the enemy's HP down and finish him off with an Overdrive skill. Remember that an Overdrive skill with a higher level results in more points.