In the SNES, PS, and Advance versions, 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, causing a multitude of status ailments to the whole party. They will also attempt to use Heal if hit with an extremely powerful attack. Heal restores roughly 3,000 HP. However, they are weak to Holy, and if Cecil Harvey has equipped one of his Holy swords, he can inflict 9,999 damage in one attack, and in tandem with Rydia's summons, the battle isn't that difficult.
In the Nintendo DS release, the battle is quite different. There is only a single Lunasaur. It opens with Bad Breath and will use it almost every turn, although it sometimes uses a physical attack instead which has the chance to cause instant death. Once struck with an attack, the Lunasaur begins an attack pattern more similar to its original counterpart, namely casting Reflect on itself and reflecting Bio spells onto the party. As it has Reflect, Rydia must resort to summoning Bahamut or Ifrit to hit the Lunasaur's weakness, but this causes it to counter with Heal to restore its HP. Once the Reflect it has cast on itself wears off, Lunasaur lapses back into the pattern of using Bad Breath almost every turn until struck, at which point the pattern begins again.
An alternate and much simpler strategy is to repeatedly use Elixirs on the Lunasaur during battle, hitting 9999 per use. To facilitate this, certain armors can be equipped to deter the effects of Bad Breath (e.g. Headbands, although weak in defense, prevent confusion).