I'm going to assume you have to catch the new "living legend" big fish that are untradable. That would be Nepto Dragon, Endoceras, Kuno the Killer, Namitaro, Helicoprion, and Shonisaurus. Now which of these fish count I do not know, since there are more than three here. Nepto Dragon is La Noscea, Helicoprion is Thanalan, and Shonisaurus is Coerthas. That much is certain. I am assuming Namitaro is Black Shroud, and have no idea what Endoceras or Kuno are, but La noscea and Thanalan are good bets.

There could be two stages to this quest - first you catch the living legends in La Noscea (Endoceras), Thanalan (Kuno the Killer), and Black Shroud (Namitaro), then after that you are asked to catch another three even more legendary living legends - Nepto Dragon (ultimate aquatic fish, special fishing spot in La Noscea), Helicoprion (ultimate dunefishing fish), and Shonisaurus (ultimate skyfishing fish) - making you the ultimate fisher of land, sea, and sky.