To possess a fish you must first collect three runes and learn level one of the Possession power. Once you complete the first mission and meet up with the loyalists in the Hound Pits, you will have the first opportunity to collect three runes, learn the skill, and possess a fish. If you are on your Mostly Flesh and Steel playthrough be sure to save the game before learning Possession.
Two runes are scattered throughout the Hound Pits complex that you can locate by equipping the heart, and a third can be purchased from Piero. Learn Possession and head over to Samuel in the boat. Equip the Possession power by selecting it with :L2:. Jump in the water and you will find several fish swimming around. Simply target one and use Possession on them. After a short while the trophy will unlock.
If you are already beyond this point do not worry: the fish are always in the water. After each mission you will return to the Hound Pits and have a chance to visit the water to possess the fish.
To see a walkthrough of the the method being performed, please see the video below: