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.
Well Apcolyptic, I wanted to answer your request for help in the Other Gaming Thread, but the character limit cut me off. Anyways.
It's been a while since I played FFV, but my guess is that you're either underleveled or you aren't using the recommended job classes (Knight, White Mage/Time Mage, Black Mage/Blue Mage/Summoner, and Thief).
I believe you should have access to the Time Mage and Summoner classes by then (both of which I HIGHLY recommend you use, they're awesome, try combining the Time Mage with your White Mage and Summoner with your Black Mage). If I remember correctly, Ifrit is susceptible to Gravity (a Time Magic spell which halves the opponent's HP, although some bosses and enemies are immune to that).
Another thing you might want to try is the Knight's Two Handed (I believe that's what it's called) ability which gives them doubled power (at the cost of not being able to equip shields) for their attacks. Also try using Ice elemental spells (I believe he's weak to Ice elemental spells, or at least that would be common sense since he's a Fire elemental summon) like Blizzard. Another option is Shiva (an optional summon/boss found in a hidden part of Walse Castle: Fire Rods make beating her easy though if you use them as items) which is an Ice elemental summon.
Or you could just try level grinding. Another idea in case you're ever stuck playing the game is to watch some of HCBailly's FFV videos on YouTube. He pretty much destroyed that game in his LP of it and if you follow him, you're guarunteed to utterly destroy FFV too.
Hi Apocolyptic! I'm guessing you don't know me but over on ZU, I'm LegendOfHyrule31!