If you are having difficulties taming this in the deep water especially when it starts running around, do what I usually do on every new map I play:
Get a Basilo (optional) > Plesi/Turtle > Tuso (Squid).
With the squid, you can look for a higher level Mosa easily & drag it to your water dino pen. You can push the Mosa in through a Behemoth gate and just knock them out safely within your base.
It’s a longer route but much safer and more reliable especially when you are aiming to get/breed high level ones.
Center tip: as they have added the mosa to the center I've found the easiest way to knock one out is find one close to the bubbles get its Agro and swim in the bubble the mosa will get stuck and it can't hit you. Also this gives you unlimited oxygen and sanctuary from being attacked by anything else. ðŸ¤˜ðŸ¼