One boss in the massive extra stage of Samidare is a huge reference to the battle with Yuki and Mai.
Despite her claiming that she is stronger than Yuki, her in-game bullet patterns are found to be less complex and easier to deal with than her fellow witch's. This irony may be purely coincidental, or perhaps not.
Mai's personality and theme song name may be a reference to the ninth circle of Hell in the Divine Comedy, which represents the treacherous sin with the frozen river named Cocyte, where the biblical traitor Judas Iscariot is being tortured for all eternity.
When you are against Mai in the second round, her sprite's appearance changes a little bit. Her little angel's wings become "demon/bat"'s wings, they are still white though. It is the sign that she is releasing her full strength perhaps...?