The Conceited Maya is a shadow in the series.
Conceited Maya is a boss found on the 16th floor of Judecca. It impedes the player's progress and must be beaten to proceed.
The Conceited Maya follows a strategy that is focused on hitting its foe's weaknesses, and then using the One More to deal severe damage with Cruel Attack. If Aigis has an elemental weakness, it will tend to focus on her as well. Thus, covering the weaknesses of the party's Personas is important to the fight.
As the Conceited Maya runs low on health, it summons a Jotun of Blood, before supporting with party debuffs. These Jotuns follow the same strategy as the Conceited Maya, but they possess the more damaging -dyne spells and often use their One More to cast Mudoon or Megidola to kill unlucky or weakened party members. Still, it is recommended that the Conceited Maya be defeated first so that the party is free to use multi-targeting physical skills.
Koromaru would be a good party member to bring to this fight, since he does not have a weakness that can be targeted by either the Maya or the Jotuns, not to mention his immunity to darkness should the Jotuns try to cast Mudoon on him on their One More. Metis is also another good choice as she has no weaknesses and decent magic. The third best choice, assuming you don't have any equipment that nullifies a weakness, is arguably Ken; he is weak to Dark but has no other elemental weakness.