To fight Oboro Bishamon and get the special ending, you need to defeat each opponent without losing a single round and using a specific EX Finisher . The specific EX Finisher required is noted below. After beating the last boss, Oboro Bishamon will appear. You'll get the special ending after the credits.

Unlockable	How to unlock
Anakaris	Use Pharaoh Magic.
B.B. Hood	Use Beautiful Memory.
Bishamon	Use Oni Kubi Hineri.
Demitri	Use Midnight Pleasure.
Felicia	Use Please Help Me.
Hsien-Ko	Use Chuukadan.
J. Talbain	Use Moment Slice.
Jedah	Use Prova di Servo.
L. Raptor	Use Hell Dunk.
Lilith	Use Gloomy Puppet Show.
Morrigan	Use Darkness Illusion.
Q-Bee	Use +B.
Rikuo	Use Aqua Spread.
Sasquatch	Use Big Sledge.
Victor	Use Gerdenheim 3.