Lunasaurs attack in pairs 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 myriad status ailments to the whole party. They will attempt to use Heal if hit with a powerful attack. Heal restores roughly 3,000 HP.
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 is not that difficult.
Lunasaurs do not start casting Reflect/Bio until one of them is hit. This can be countered by casting Dispel on one of them (if the player removes the Reflect status from both of them, they will re-cast Reflect on themselves). They also get hit with their own Bad Breath attack when a party member has Reflect up.