If you have a tusoteuthis you can knock this guy super easy out. A tuso does 10 torpor per second while you are grabbing a dino, so a lvl 150 mosa takes about 50 min to knock out. You just can be afk and then he will be knocked. You can also bring someone else with you and he can tranq him out while you are grabbing it with your tuso.
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