Here is the full list of all 13 Extreme Exorcism trophies - there are 9 bronze, 3 silver and 1 gold.
Unlock all rooms
Die 1000 times!
Finish five rounds without missing a shot
Kill five ghosts with one harpoon
Kill a total of 1000 ghosts!
Unlock all weapons
Complete Arcade mode
Defeat the final boss without losing a life!
Complete all challenges.
Manage to amass thirty ghosts on-screen!
Kill ten ghosts with one explosion
Exorcise ten ghosts at once
Jump on five bullets in one round