The first battle is scripted so that the party cannot defeat Baugauven. Any physical attack or magic will deal very minor damage to him. The party must try to survive the onslaught of attacks (that include Burning Slash and Fira) until Baugauven uses Heat Wave, which leaves all party members at single digit HP. He will then use Final Backdraft, ending the battle.
The second battle occurs on Mt. Gulg. Baugauven can hit for about 400 damage. Burning Slash may do heavy damage damage to the party, about 600 damage to the front-row and Burning Slash can be used twice. Heat Wave can do about 500 damage to the party. Furthermore, Baugauven will counter most attacks with Fira.
White Mage with Cura can help remedy the problem of his attacks such as Burning Slash. Even then at this point the party likely can survive these attacks by healing all the turns. Also, a Black Mage with Blizzara will inflict massive damage on Baugauven. Attacks such as Strike, Aurablast, Smash, and Darkness can greatly damage the general, rendering the threat of his counter even more feeble.
Having Graham in back row and let him cast Draw Attacks while having another member heal him with items. This will make Baugauven focus on one member, who will get healed constantly. Eventually he will use Final Backdraft to end the battle, after which Graham will battle Baugauven alone and defeat him with Zantetsuken.
The third and final battle takes place in Rended Void. Most of his attacks inflict major damage. Rage, Rend and Stun are typical moves that can either deal physical damage or stun several members. Pox will damage the whole party, dealing about 1500 damage to a front-row member at level 60 and can inflict some negative status. Firaga, which can be used to counter attack, deals as much as Pox to a single member or half to the party. Heat Wave inflicts more damage than Firaga to the party. Final Backdraft has the highest damage output. It can instant kill a single party member with an insane amount of damage.
This fight can be won with a little effort if the party is highly leveled. Also, Baugauven is weak against Water and Ice so equipping weapons with such element while using Phantom Rush or Midareyuki can damage him well. One or two healers are needed to buff the party and heal them.