The key to good results in battle is, like in many turn based RPGs, using elemental advantages in order to turn the tide of battle, of course. Using moves your opponent is weak against will obviously do more damage, but you have to avoid using moves they're resistant to. Some enemies will even absorb the damage you do of a certain element, and take it all as HP. Exactly the opposite effect of what you want, so keep an eye on the enemy's resistances and weaknesses on the right of the screen.