In order to unlock Babi-Onna, you need to evolve the Summon Night weapon (starting weapon of Syuuto). That weapon requires a lvl 2 duplicator item to help evolve.
I got Babi-Onna unlocked when I did all of the Syuuto achievements together. Once you have this character go to whatever level you want and survive for 15 minutes.
*Credit to The S Bot 9000 for the update:
You can also unlock her by using the spell: "Vogue" using the scrolls of morbane (secrets menu)