In order to get the "Thus is Thy Fate Sealed" trophy in Burly Men at Sea, you need to leave the Whale without putting on the barrels, defeat the jellyfish and interact with the Musical Wizard.
(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 you will unlock:
-- Swim right for a moment. Stop and swim left. Swim to the right a little again until you see an island.
-- It's not an island, it's a jellyfish! When the tentacle is on its head, move your cursor over it and hold X until one of the Men heads over there. Repeat for the other tentacle so both are being held in place.
Once the dialogue is finished you will unlock:
-- Hold a trigger (or shoulder button on Vita) to open the curtains
-- After the dialogue, interact with the Musical Wizard again
At this point you will unlock the trophy. You can either quit out to the village from the main menu or you can see the run through to the its conclusion, which will eventually put you back in the village anyway.