I checked now, and according to the Official Guide, Zodiark does not actually become completely invulnerable, rather it casts spells that protect it from all magic and all physical attacks- almost the same thing, except the spells fade over time, though it will keep recasting them, so you have to constantly keep track of what to strike it with. It also has a shifting elemental weakness. Sounds like a lot of work, but doable. The guide does recommend killing it with a Chain Quickening before its HP get low enough that it starts casting those spells (when it has about 1/4 HP left) though. That would be at about 84,300 HP.
(And WHAT THE HECK is that thing supposed to be? It looks like a bug hanging from a wreath to me! Definitely the most absurd design in the game I’ve seen so far. At least the other Espers were somewhat humanoid.