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
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.
The trick is to argo one, have him chase you into an underwater cave where he will not be able to fit through the door but his long neck and head does. when you do this he will not de-agro, you can then get a clear shot from the cave with a bow and tranq arrows
Trapping- it's a 3 for 1 trap. Trap will work for plesio, moss, Squid. 4 sides of behemoth gates. 4 corner inside trap with pillars higher than gate. 3 Celling on each pillars going center of trap. So only a small gap in center. Now take a small angler or ichy or shark. Lure dinos in and get out from top and close door.
Early game taming trap for big water dino. Now your problem is getting it tamed after that. They take a lot of ressources to tame.
I would suggest plesio and kill other stuff with it like alpha to get black pearls and Lure squid in same trap.
For Ark Mobile: get urself a basilosaurus if u can't unlock the scuba set. Find it and then stay a little bit away from it and it can be done easily with tranquilo arrows and a crossbow. Get some Rex kibble or meat