Here is the full list of all 13 Extreme Exorcism achievements.
Complete Arcade mode
Unlock all rooms
Defeat the final boss without losing a life!
Complete all challenges
Manage to amass thirty ghosts on-screen!
Kill five ghosts with one harpoon
Kill ten ghosts with one explosion
Exorcise ten ghosts at once
Jump on five big bullets in one round
Unlock all weapons
Die 1000 times!
Kill a total of 1000 ghosts!
Finish five rounds without missing a shot