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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.

More Mosasaurus Taming & KO Tips