For the love of god, do not fight them in water! A level 4 baryonx nearly killed my Theri because the baryonx had stunned him. No matter how shallow the water is, do not even think about fighting one. They can stun you and knock you off your creature.
So, I began playing Ark, and happened to build a base right next to where a Baryonyx lived. My friend was gathering things from the other side of the river, and led one right to the base. It had been like a Jaws movie for the next few days. Well, I have formed a plan to get rid of it. Wish me luck!