1: Do not fight them in water under any circumstances
2: Lure them on to land
3: Use a bola
4: Attempt to Tranquilse with bow and arrow or better
Remember: They can only be tamed with fish meat and they usually kill all the fish in the area so you should probably have some prepared beforehand.
Baryonyx are quick like Allosaurus and do just as much damage (but don't get a pack bonus). They don't use oxygen for swimming and can sprint in the water. Right click in the water does an AoE stun that lasts about 10 sec. Their 'C' is a... Taunt? They also jump and you can fire a weapon from their back.
The Baryonyx is a large crocodile-like predator. While it might lack in attack power, its ability to swim extremtly fast makes it a fierce opponent — especially with its ability to travel on both land and in water.