Eat a rage flower near the plesiosaur. Then swim up to the top of the ocean it won’t be able to hit you. Because it’s so high up then what it is suppose to come up to. Just be careful of nearby fish and other Dino’s when using the rage flower.
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
If trying to tame one make like a wyvern trap on the bottom on the ocean and hive someone else shut it. I use a sarco to lead it in the trap. On the center you can make the trap right next to the air bubble to escaped in the Airr away from any attack range and have a keypad to shut it.
If you’re on the center, go to the east water dome. There’s a small gap of water between the dome and the rest of the ocean where sea creatures can’t reach. The tricky part is when it starts running away after reaching a certain torpor level but this makes it a little easier.
Make a taming pen at the bottom of the ocean near a plesiosaur spawning place made of stone 7x6x6 with sealings,foundations,doorframes and a behemoth stone gate.Then use a tough underwater mount to kill the plesiosaurs you don't want, because they spawn in groups of 2 or 3.After that kite the last one into the pen,get out using a doorframe,close the behemoth door and you can hit it easily.Use this strategy to tame plesios and even harder dinos like mosasaur.
If you're on the Center there's multiple spots where plesiosaurs are glitched and can't move. One is at the redwood forest shoreline near a rock and the other is somewhat in the center islands underwater. The second one has one on top of the other so kill one or tame both.
These poor misunderstood plesiosaurs. When they go up to you, they try to give you a kiss but their huge teeth kill you instead. When taming, be sure to use the invisible depth barrier. They will only go up towards the surface if they are tamed.