There are 25 types of fish to find in the game, and this trophy is for catching 14 unique types. You will need to upgrade your fishing rod at the workshop near the entrance to Trans Town, as some Fish will have a lot of HP, in which you don't get enough time to catch them. This can be done at any point, even postgame or after your second playthrough, so no rush.
I'll list below a full list of areas as you come across them in story progression, and what you can find within each area. There are some fish you can find in all areas, so I'll put them under an 'All' tab, then onto the unique ones. It's worth noting that some fishing locations within the episodes are only available after beating said episode, and going back to it in free roam. Mt Corvo for example.
All locations -
3-Fork Tail Killifish
Armored Crab
Fork Tail Killifish
Gastropod
Glistening Suary
Kragen
Sea King Family
Smiley Jellyfish
Treasure Pearl Clam
Trans Town -
Panda Shark. You can also find the Panda Shark in side quest location, Baratie. You'll typically fight Mihawk here for the first time.
Punk Hazard -
Bone Fish
Hammer Sea Anemone
Shark
Skull Knight
Alabasta -
Adventure Fish
Balloon Catfish
Sandora Catfish
Skull Knight
Enies Lobby -
Hammer Sea Anemone
Marine Flounder
Fishman Island -
Adventure Fish
Gyoriiza
Hammer Sea Anemone
Old Deep-Sea Fish
Shark
Skypiea -
Lovely Angel
Octopus Balloon
Sky Fish
Sky Lobster
Mt. Corvo -
Bluefin Elephant Tuna