Much more powerful than its previous form, the Dark Dragon has two attacks, a melee that does regular damage, and Dark Breath which does moderate Fire-elemental damage that is capable of killing the party in a few hits. The player might want to grind a bit outside of the cave before this battle, because if one wrong move is committed, the party is dragon fodder.
In the non-DS versions, Dark Dragon is susceptible to Tornado. Using this will reduce his HP to one, allowing the player to kill him with a simple attack after.
Cid should use a Spider Silk, while CecilcoversTellah who starts casting Firaga, and Yang uses a Bacchus's Wine on himself. Once Yang goes Berserk, he will unleash a strong attack, doing well over 450 damage. Once Tellah's Firaga goes off, the fight should be over. Focusing Yang before the Bacchus's Wine is risky, but allows for less chance for a need of a follow-up attack after Tellah's Firaga.