Elma is not that much of a threat to deal with, though her biggest threat will be her Haste spell. The party should focus on taking out her companions first before targeting Elma herself. If anyone's HP falls below 300, one should heal with a Hi-Potion. If anyone has learned the Songstress ability Sleepy Shuffle, it will make this fight even easier, since Elma is not immune to the Sleep status.
This battle is much more difficult in comparison to the first battle. Elma now uses all four -"ra" elemental spells, so if possible, one should aim to equip any dressphere, Garment Grid, or accessory (preferably Force of Nature) to absorb elemental damage. It's not worth casting positive statuses, as Elma simply dispels them.
It is also best to not use any heavy magic-using dresspheres (Black Mage, White Mage, and Gun Mage in particular), since there is a great chance of them being silenced by Hush Grenade. If Elma uses Not-So-Mighty Guard one should counter with Dispel on Elma.