Security Eye counter all attacks with the Alert ability, which summons either a Stone Golem, Chimera, Naga, or Flamehound. Any attack made when an enemy is on the screen that targets the Security Eye results in a Beam, which deals magic damage. One of each kind of Security Eye appears in various monster-in-a-box encounters. Security Eye only attacks if provoked.
Because of this creature's attack pattern, there is only one real way to make it through the fight without taking damage. That is to wait until everyone's ATB bars are full, and hit it with the party's weakest character, and use the remaining characters to kill the summoned beast. For maximum experience one should stop attacking once the summoned beast has been defeated so the weakest character hits it again. Via this method, depending on the party's strength and the beast it summons, the player can walk away with plenty gil and experience while taking no damage.
As Security Eye will not attack unless provoked the encounters with it can be a great opportunity to restore HP/MP with Rosa's Pray. Everyone else should defend and Yang use Focus twice. Yang can equip the Lightning Claws to expose the Security Eye's weakness. Alternatively, Rydia can summonRamuh, which should kill it in one hit. Palom can also use Cry without provoking it to attack.