This dinosaur is a very intricate but interesting dinosaur to get. I did find it near the shore line as it had seen me and wanted to eat me. However I had 5 tranq arrows which you can get at lvl 21. I shot all 5 and he fell to the ground. Very good dinosaur to tame especially in the water. It beats anything in the water even with its stun strike. I recommend using this dino to fight. I have one named Juju. One like equals One love for Juju
Bringing a simple raft cage to the swamp should allow you to easily trap and transport this guy to an appropriate area to knockout and tame.
For some reason (bug?) you can’t be damaged while driving the raft, even when this guy is standing on top of you! (PC)
If you have access to them, get bolas and then hit it with a bat (at the tail, preferably). The reason you don’t want to attack from the front is they can fight back at the front, no exceptions. Usually you can hit them enough times that if the bola wears off, you will have scared the Baryonyx into trying to flee anyways, although possibly 35% of the time you can knock them out before that happens. But before doing any of these bring at least 3 stacks of 40 fish meat, as despite being carnivores, Baryonyx will strictly only eat fish during the taming process. Hopefully this helps