In order to get the "Fountain of the Faithless" trophy in Burly Men at Sea, you need to leave the Whale without putting on the barrels.
(Remember to make cross saves before trophy related decisions to drastically speed up your play throughs).
Here's the steps from when you enter the Whale, which is an unavoidable incident at the very beginning of the game:
-- Talk to the girls by the fire
-- Head left and go through the door behind your ship
-- Scroll right, get through the dialogue
-- Interact with the uvula, get through the dialogue
At this point the trophy will unlock.