First off, you need at least 5 pts. to use this special attack, so first get that.
Second, go to whatever boss you would like to exorsize. Grab a part of the boss that takes damage, then you must press and hold the L3 and R3 buttons (which are activated by pressing down both analog sticks on the Dual Shock/2 controller). If you did it correctly, you will see 3 scarfs grabbing the enemy now. Hold L3 and R3 down until it looks like something is happening to the enemy (which is now becoming exorsized).
If you exorsized the demon correctly, there will be a pointy nosed smiley face in a black cloud hovering around the battlefield. Then destroy the boss. That's it!
NOTE: All exorsized demons will end up becoming part of the bell in the center room, where you can try different textures on them and stretch them out in that mode. You will not get the ending door (which contains the credits) until all the demons are exorsized.