Besides the giga this is the hardest dinosaur to tame, note you will need a lot of narcotics and food. Before you begin the tame I recommend at least 2 to 3 full scuba suits for obvious reasons. You need to have at least a Ichthyosaurs or Megalodon, so you can actually move around and find a decent one. Once you find one you want to tame simply start shooting at it with the crossbow. Now right when you get his attention swim up, you should notice the Mosasaurs stops following you after a certain height. The Mosasurs cannot go higher than wherever it stopped. So simply park your water Dino above it and keep shooting it. If it runs off keep doing the same thing over and over again. Sooner or later you will take him down. Good job! Then simply use this app to figure out how many narcotics/food you will need to tame it. Once it is done enjoy your king of the water.
I recommend a trap. Make it out of foundations, pillars, ceilings and a behemoth gate all in stone. Use an icthy with levelled speed and health to lure it in and close the gate behind it. Then simply tranq arrow it until it’s down. Preferably use at least an apprentice crossbow, prim will take way to long
Tame some use less creatures and feed to mosa and stay relaxed and feel free to knock it out
WARNING KEEP ALL CREATURE S IN PASSIVE AND ALSO HAVE A GET A WAY RIDE IF IT AGRO ON YOU OR TRYS TO KILL YOU AFTER KILLING ALL OTHERS
I PREFER BASILO FOR THE USELESS PART CAUSE THEY HAVE MORE HEALTH AND ITS PASSIVE TAME if you want any creature is ok