I'm not a Dragoon, but I do have it unlocked. I found this
HERE:
The Offensive Wyvern: Has a random elemental breath attack, and is used whenever the Dragoon does a Weapon skill (the elemental attack doesn’t include light or dark)
SUB JOB NEEDED: Beastmaster, Monk, Ranger, Samurai, Theif, Warrior, and Summoner
The Healer Wyvern: The first type of ability that a Healing Wyvern has is Cure Breath. The Wyvern casts this upon the Dragoon whenever the Dragoon uses a weapon skill. This Cure breath will cure any status ailments the Dragoon might have. But the Wyvern will only cast it if there is something to cure. The second type of ability is Heal Breath. Whenever a Dragoon casts a spell the the Wyvern will cast heal breath and it will replenish some hp’s of its master or a party member, but only if they are below 1/3 health.
SUB JOB NEEDED: Black Mage, Red Mage, White Mage
The Miltipurpose Wyvern: Whenever the Dragoon uses a weapon skill, the Wyvern will use its random elemental attack on the target. And when the Dragoon casts a spell, the Wyvern will cast Heal Breath, but will only be used if they are below 1/5 health.
SUB JOB NEEDED: Bard, Dark Knight, Paladin, Ninja