Leviathan has two forms, and approximately every three rounds it will switch. In High Altitude, Leviathan automatically evades all physical attacks, and uses Blizzaja to deal major Water-elemental magic damage to the whole party, along with Envy to reduce attack and defense, both physical and magical. In Magic Resist Form, it will use Bite, The Last Light to deal physical damage, and Consume Life to damage and inflict Doom, the latter two striking all targets, while having high magical defense. It starts out in High Altitude, without the inherent evasion of said form.
Due to the forms used, it is highly beneficial to have a group focusing on either physical or magical damage, using Default and healing while not attacking. Also, due to the high, group-wide damage, it is a good idea to group-cast Cura, or an equivalent, nigh constantly. This is also helpful to charge Rejuvenation and use it later to cure Doom on the party, by setting Doom Cure part to it before battle. The Spiritmaster's Enigma can be used to avoid damage from High Altitude form.
It is also possible to use a strictly magic-oriented team against Leviathan if they are equipped with the Black Mage's Pierce M.Defense perk which will allow the party to damage him even in his Magic Resist form.