Cloud: I couldn't finish 'em. Looks like this's gonna get complicated.
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Lucil's attacks are mostly physical in nature - however, she can also perform an attack called Harbinger, which causes Doom. The easiest way to counter that is to either kill her quickly or to use Dark Knights, since they're immune to Death, thus countering Doom's Death effect.
Using Force of Nature or any elemental absorbing/nullifying accessory, Dressphere, or Garment Grid helps as well, since Lucil uses elemental items. Combining Dark Knight with Force of Nature pretty much ensures victory, as the only way for Lucil to defeat the player is to physically attack, which is not much of a threat.