You'll acquire this trophy by finding and speaking to the Fisherman NPC at all his locations. The list of locations are:
Harikoa - He is on the right side of the town, near the pond of water.
Lilac Lagoon - In the middle of the area, next to the bonus dungeon. You need the Snorkel to be able to get to him at this location.
Airey Bay - Once you enter this area from the plains, you'll be on a big beach. Enter the water with the Snorkel, and go up a couple screens. After a few screens, you'll see the fisherman along the beach, fishing.
Mount Janszoon - Upon entering this area from the Plains, simply go left and then up. You will find him standing next to the water fishing.
Maru Forest - Upon entering this area from the Plains, just keep going right. Enter the water once you can and go to the right again. There you will find the fisherman again. Simply get back up onto the land and talk to him again.
Butler's Cay - Once you swim to this area, follow the landscape down and around the area while in the water. You will find a path to get up onto land and then follow the screen down. There you will find the fisherman again.
Plains - From the beach in Harikoa, simply enter the water and follow the screen to the right. Once you enter the Plains, follow along the landscape, and there will be a spot where you can get back onto the land and the fisherman will be fishing right next to the landing.
Trail Farms - After you gain access to Trail Farms, go to the right of the area until you find a big silo. Once you find it, the fisherman is right next to the silo fishing.
After that, you can return to his home back in town. Talk to him to receive a feather and your trophy.