In order to get the "In Need of Assistance" trophy in Burly Men at Sea, you need to leave the Whale without putting on the barrels, allow the jellyfish to defeat you and make sure to break out of the bubble by moving the seals away from each other.
(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! Wait for the jellyfish to grab a Burly Man and interact with the tentacle to make it drop him again. Do this three times for each Burly Man.
Once the dialogue is finished you will unlock:
-- Hold R2 (or R on Vita) until the Seals are far from each other and change form.
Once the dialogue is finished 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.