The party will begin with whatever HP and AP they had at the end of the fight with King Guera.
As usual, an Elementalist is advisable. The party should equip Rock Shields and, if available, the Soil and Fire capes. Accessories to nullify status ailments are also helpful for dealing with his Sidewinder attack. The party's damage dealers should be equipped with abilities that target Asmodeus' weakness to Water.
If the player has Lux, it should be cast at the start of the battle, and Mysterio should be renewed whenever it wears off. Asmodeus' physical attacks are Earth-elemental and have a chance to poison the target. His most dangerous attack is Sidewinder, which deals Earth-elemental damage and randomly inflicts Confuse, Paralyze, Silence, Poison, and Curse. He can also cast Silence, Petrify, and Death. Asmodeus also uses Moonlight Curse, which results in negative Psyched Up.
Asmodeus' six snake heads do not attack, but they must all be destroyed before Asmodeus takes damage. Magic Might or Waterga are useful for this purpose, and the Elementalist's Amplify and Augment will make this more efficient. Asmodeus is capable of dealing a lot of damage in a short amount of time with his multiple spells, and it can be difficult to recover if the party healer is affected by status ailments. Asmodeus can be Silenced to slow down his magic attacks.
Asmodeus can actually be killed before killing all the snakes on his head, this is because they both share the same health, this only applies to Asmodeus's 4 Heroes of Light version, since in the Bravely Default version, the snakes cannot be killed.