The Dragon mainly strikes at the party with its physical abilities. Bully strikes the target with the lowest HP for heavy damage, and Mow Down strikes the entire party for damage. It will occasionally Brave, using both abilities in one turn.
With the Dragon's ability to use Mow Down and Bully, it's recommended that the player have a White Mage that can use the spell Protect. With the Dragon's low M. Defense and weakness to Water, it would be best to have a Black Mage with the spell Blizzard to do decent damage. For the physically members of the party, use Special Moves to build combos and lay into him after he Braves