Ah. Well, from my own experience, Mystic Knight isn't that much good other than for utterly destroying everything with the Chicken Knife, but maybe you'll find more use for him.
I think Byblos may be weak to Gravity, and having Ifrit around is pretty nice. A tactic you may want to consider using is a Firaga ala Fire Rod. Basically, you equip a Fire Rod before the battle, go into the items menu in battle, go up (for instance, from the top of the menu, if you press up, you can access your weapons. Double click on the Fire Rod and it will allow you to choose a target. And when you do choose your target, you get a FREE Firaga spell and trust me, Firaga is INSANELY powerful/broken at that point in the game). That'll probably decimate him in one hit.
Also, I believe if you use Ifrit on him, he'll be stunned for a while so that he can't do anything.
Also, try using a Fire or Fira Spell Blade on Byblos. Another option is to use Haste on your party (it makes a party member's ATB bar fill up faster which is actually a lot more useful than you'd think) and Slow or Stop on Byblos.
If that doesn't help, the only other option I can think of would be to grind for some levels and try the above tactics again.