Byblos inflicts many status ailments, so proceed with caution. He constantly inflicts Confuse, but he also drains the party's MP with Magic Hammer and half their level with Discord. He will occasionally Counter physical attacks by casting Protect on himself and magical attacks with casting Toad on the party.
When Byblos is at low HP, he will occasionally counter with Drain for approximately 300 damage, so the party should not attack him at this point, unless they can deal more damage than he can drain. A Black Mage should spam Fira, since he is weak to Fire magic. A Mystic Knight can also help. It is not recommended using Ifrit in this battle, as, contrary to Apanda, Byblos will counter Ifrit's attack by casting Toad and Confuse on a character.
A safe, quick, easy way to win is to use the Blue Magic spell Death Claw. This will take him down to single digits, and make killing him easier. Additionally, using a Fire Rod should defeat him quickly; these can be bought in Karnak. Additionally, Ifrit will deal heavy damage on Byblos, and around four-six summonings of Ifrit will defeat Byblos.