Here is the full list of all 39 Cathedral achievements.
Buy the Onyx armor
Find all armor augmentations
Buy the Tourmaline armor
Complete the game without upgrading the armor
Kill Ardur
Find all ammo upgrades for the Magnus Apparatus
Find all ammo upgrades for the Flintlock
Find all map pieces
Destroy the Conduit
Have more than 50 000 gold stored in the bank
Find and activate all portals
Kill 150 skulls (of any kind)
Kill Nidlong
Acquire all health bottles
Return 100 books
Kill the blood knot
Kill Thalia
Kill Oloc
Find all hearts
Find all charms
Return 80 books
Acquire all Ouroboros amulets
Slay all gargoyles
Have more than 25 000 gold stored in the bank
Return 60 books
Destroy an electric orb in Necromancer's den using the lantern
Kill Salemacke
Die one hundred times
Return 40 books
Have more than 10 000 gold stored in the bank
Kill the Necromancer
Kill 100 skulls (of any kind)
Return 20 books
Kill 50 skulls (of any kind)
Kill 150 blobs (of any kind)
Buy the Emerald armor
Kill 100 blobs (of any kind)
Kill Augr
Kill 50 blobs (of any kind)