A Purple Mirror is initially summoned by Mayone during the fight with her. They can later be found in random encounters on the first floor of the Amami Monolith.
Devil Survivor 2
"A mysterious mirror that mediates curses. If you don't forget about its existence by the time you turn 20, you will fall victim to misfortune. Mirrors are often used as tools of religion, but this one is an implement of curses. It may seem like mere foolish superstition, but the unfounded anxiety it causes can be said to reflect the human fear of death."
—Devil Survivor 2 Compendium
Purple Mirror is the strongest member of the Ghost race, and is notable for its multiple immunities. If one were to impart Phys Repel and Force Null/Drain/Repel to it, it will become immune to anything save for Almighty attacks, a feat that can only otherwise be accomplished with Metatron, Frost Five and Titania.