Instructions
Equip members of your party with armor that has "Auto-Phoenix." This will revive them when they are felled by a 10,000-needle attack from Cactuar King. Since this enemy will only attack one of your party members at a time, equipping this type of armor will ensure you will be at full strength after each turn.
Use an attack such as "Blitz Ace" or "Attack Reels" on Cactuar King to do massive damage to him. Cactuar King is immune to magic and will dodge many regular attacks.
Attack Cactuar King with "Flare" if some of your party members have this attack. Because it is non-elemental and not magic it will help in taking down this enemy. Although Cactuar King can dole out massive hits, he can't take too many himself because his hit points figure (HP) is low. It should only take a handful of direct hits to defeat him.