After numerous Leviathan kills, I finally learned Spell #49 Veil of the Whorl from Leviathan.
I ignored some mechanics because, other than throwing me into sea, Leviathan could not one shot me and I can heal myself as a blue mage healer. I knew I should have been attacking the spheres rather than Leviathan when they were up, as Leviathan takes 0 damage then. Providing I have enough hp (which as a blue mage healer is easy to restore using Pom Cure with Basic Instinct on in soloing multiple-player duties), I can survive any one-shot attack from Leviathan (with Mighty Guard on). The only thing which can KO me is Leviathan or one of the adds causes me to go overboard.
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