The Blue Dragon, also known as the B.Dragon, is one of the four elemental dragon bosses in Final Fantasy II, found in the Jade Passage guarding a treasure chest containing the Cat Claws. It can also be found as a normal random encounter in a secret room in Pandaemonium.
Cast Shell and Protect on the party to ward off damage from Blue Dragon's powerful Thunderbolt 16 spell and physical blows. Equip some Poison Axes and use Scourge to take advantage of its weakness to Poison. Heal your party members as necessary. Using this strategy, the Blue Dragon should fall quickly.
An alternate method of winning is to simply cast a level 8 or higher Teleport.