The Priestess Full Moon boss, Arcana Priestess, is encountered on May 9th. This Shadow has no elemental weaknesses but is susceptible to physical attacks. It uses electric attacks (Zio) and can inflict Shock. Equip accessories that boost Electric resistance if you have them. Your party should ideally consist of Yukari (healing/wind), Junpei (physical/fire), and Akihiko (physical/electric). Focus on dealing consistent physical damage. Use Personas with physical skills like Bash or Cleave. Keep your HP high with Yukari's Dia spells. If a party member gets Shocked, use a Dis-Charm or wait for it to wear off. This fight is a test of attrition and consistent damage output.
