Black Dragon is a Soul of Rebirth enemy in Final Fantasy II. It is also a boss in the Southwest Arcane Labyrinth. They attack with powerful physical blows, and use Flare XVI to deal massive damage to a single target.
Since Minwu is in the party, a useful strategy is to cast Dispel on the Black Dragon to lower its magic resistances, rendering it vulnerable to status ailments and thus much easier to defeat. Otherwise, the Black Dragon has high defenses and no weaknesses and can be quite difficult to kill. An alternate method is to simply use Minwu's Teleport spell, if it is level 8 or higher, to defeat it in one go.