Here is the full list of all 13 Extreme Exorcism trophies - there are 9 bronze, 3 silver and 1 gold.
Exorcise ten ghosts at once
Kill five ghosts with one harpoon
Finish five rounds without missing a shot
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 ten ghosts with one explosion
Jump on five bullets in one round
Unlock all weapons
Die 1000 times!
Kill a total of 1000 ghosts!