My trusty sarcosuchus made knocking my plesi exceedingly simple, for three reasons. The sarco is fast, it ascends quickly, and you can shoot from its back. Once I separated my plesiosaur from her friend and killed it, the procedure was simple. When the plesi reaches a certain height it begins to flee. I dragged her up then filled her with tranqs until she aggro'd again. Repeat process until unconscious. Simple with sarco.
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.