Mephilia frequently casts Summons Soldiers (which calls Legion Impaler and Legion Archer) throughout the battle. She usually uses normal attacks, which deal significant damage. She also summons Girtablulu, which deals heavy damage to the whole party.
The party can just keep attacking Mephilia. Whenever Mephilia casts Girtablulu, immediately heal with Cura or Cure. The legioners she summons can also deal high damage, especially the Legion Impaler's Execution, which can deal more than 500 damage. Dispatching them with group-targeting magic like Thundara and Fira is recommended to avoid Mephilia's Girtablulu being much a greater threat.
Mephilia tends to cast Girtablulu around every 3rd turn, so the player can use that time to perform a Default and mitigate the damage, then heal on the next turn with Cura and use Brave to unleash major offensive during the time she sticks with physical attacks. Whenever she summons legioners it is recommended the player fells the Archer, as she can inflict status ailments like Confuse which can be fatal coupled with Girtablulu's massive power. She never uses either Brave or Default, so offensive and defensive maneuvers are easier to perform.