In the original SNES, J2e, and PlayStation versions, Asura casts Cure 3 and Cure 4 on herself periodically during the battle, making it difficult to inflict lasting damage on her. She also counters attacks with a physical that will likely do over a thousand damage.
Asura's AI script is quite different in the Advance release. She begins the battle by casting Protect on herself, and casts Curaga and Life on herself throughout the battle. Asura's only attacks are Protect, Curaga, and Life - she only attacks the party when they attack her, thus giving the player as much time as they need to heal themselves before continuing the battle, should Asura prove too strong.
In the DS release, Asura begins the battle by casting Protect, but otherwise, the battle is identical to the Advance release, although Asura's attacks do more damage.
In the SNES, J2e and PlayStation versions, the only way to defeat Asura is to have Rosa cast Wall on her, which will bounce Asura's Cure and Life spells onto the party, healing them. At this time it is merely a matter of wearing down her considerable HP.
In the GBA release, merely casting Reflect against Asura will bounce her spells onto the party. Asura also casts Protect on herself, but this, too, will be reflected. In the DS release Asura's physical attack is powerful enough to kill some party members in one hit, and since Asura absorb most elements, the favorable strategy is to summon Dragon when Rydia is under the Bluff Status to deal large damage, provided that the player gives Rydia the Bluff Augment.