Lunasaurs attack in a pair and guard two Ribbons. They cast Reflect on themselves, and bounce powerful Bio spells off themselves, doing about 2,000 damage to a single party member each time. Possibly the most fearsome thing about them is their Bad Breath attack, inflicting a multitude of status ailments to the whole party. They will attempt to use Heal if hit with a powerful attack. Heal restores roughly 3,000 HP. However, they are weak to Holy, and if Cecil is equipped with a Holy sword, he can inflict 9,999 damage in one attack, and in tandem with Rydia's summons, the battle isn't that difficult.
Lunasaurs don't start casting Reflect/Bio unless one of them is hit with a physical attack. They also get hit with their own Bad Breath attack when a party member has Reflect up.