In order to get the "The Path of Waiting" trophy in Burly Men at Sea, you need to interact with the girls by the fire twice once you reach the Whale.
(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
-- Talk to them again
At this point the trophy will unlock.