Elizabeth is the MOST difficult opponent in the game. Besides Nyx Avatar, she's the only enemy that can survive a direct hit of Armageddon (9999 damage, which is pretty much the damage cap in this game).
If you attempt to fight her while equipping any Persona (or equipping an accessory) with a Repel, Absorb or Null attribute, she'd automatically start the game by casting Megidolaon that deals 9999 damage to you, and practically spam you over and over again until you die, that is if you had Enduring Soul or the Spirit Bracers on to save your life the first time around. Bringing along your party members also makes her do this, since by the end of the game, they would have Null resistances.
The only way to avoid this is to equip a Persona that doesn't have the above aforementioned characteristics. Problem is... Personae that don't have Null, Absorb or Resist are pretty rare (not to mention low-leveled and weak at first). The only ones that I can recall from the top of my head are Kikuri-hime and Anubis.
And then you'd have to fuse them properly to make them inherit the best elemental spells you can use, since Elizabeth changes her Persona and her weak spot/Null attribute every now and then. That would take a looooot of time. And then there's also the time consuming task of leveling up your Persona to match Elizabeth's insane stats.
That's where Orpheus Telos comes in. He automatically comes with a strong resistance to ALL attributes. Not Null, Repel nor Absorb... but just Strong. That would let you enter the battle with Elizabeth without her Megidolaon opener and survive the fight throughout. Though, the challenge still lies in fusing the right Personae to give Orpheus Telos the right spells and skills and buffing his stats up.
Not to mention that the requirement for unlocking him is to max out all of the S. Links (including Aeon) in one playthrough. FES makes it easier to pull off S. Links, but it's still hard in the long run.
That being said... no, I still haven't defeated her....
