The method i used was to aggro him and use a Basilosaurus(big whale) and go to the surface where he will just keep reggening and while the plesiosaur is focused on my Basilosaurus i just get out my crossbow and pelt him with arrows
They can't fit through the resource caves' entrances. Just lure it into one and pull out your crossbow/harpoon gun for the knock out. Just be aware of any nearby megalodons, as they can fit into the cave easily and ruin your swimming session.
There is a glitch at the redwood on the center, where plesiosaurs will spawn really near the coast and whole groups of 2 or 3 are glitched in the water, meaning you can knock out multiple plesiosaurs at the time.