Note: Names may be tentative. These were found within the Pirate files. The files suggest that they will be shown in your Treasures.
Yellow Tang
Bermuda Chub
Blue Chromist
AnthiasTuna
Parrot Fish
Marlin
Sand Tiger Shark
Coelacanth
Hatchet Fish
Lion Fish
Atlantic Wolffishs
Black Chimera
Dragon Fish
Goblin Shark
Angler
Lump Fish
Mega Mouth
Fogbell
Fire Dragon
Glittering Girl
Mossy Moses
Speedy Lou
Also found out that there are story events for collecting all of a certain treasure category. However, it was either removed or it never worked.
It is also supposed to tell you the fish's weight, xp and gold.
There's also a regular lure and a legendary lure.
Fishing has a reputation system.