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