A good way of looking for these things (mobile): sweep the border of the map and the ocean floor, using an ichthy to keep everything away. Once you find one, park your ichthy somewhere, then swim up to the depth limit of the mosa (you might have to test where it is though, be careful, mosas can swim up FAST). Being off the ichthy will catch its attention. Swimming up to the depth limit will cause it to Aggro off of you, so go back and forth with going to its depth limit, attracting it, and swimming back up to fill it with tranqs. The basic idea is attract, swim up, fill with tranqs, repeat. Hope this helps!
An easier way is go on a itchy and find the nearest ammonite and hit it and them go slowly with the rage effect until you find one and yes i know a lot of sea creature will come so be carful when you do it (maybe you can find a squid like i did)