Using the Targeting System is a must if you want to take on difficult Quests. Tap the icon of a specific enemy to focus your attacks on them.
In later Quests, you'll need to remove certain types of enemies first to make the battle easier for your team. For example, if there is a Healer on the opposing side, you may want to take the Healer out first or he will continue to heal his teammates. In other battles, you might want to take out the Bard if he uses Reflection Shields. Those Shileds will reflect your powerful attacks back and damage your team.