When i went ou for search of mosa for first time i found a alpha mosa that the the first miss i saw . I fried to kill it but it got despawned .Till now i have seen all alpha creatures.the first alpha was alpha rex .
They spawn south on the island. Between the land and the barrier, when found, use a crossbow to get its attention and use your mount as bait (Recommend a basilo or another mosa for their high health). Once it agros on your mount, swim up and start tranqing it. Their torpor drains fast so wait a while until it reaches 40% and spam some bio toxin or narcotics in. I recommend starve taming as you could easily lose your kibble if you go away for a while.(Make sure your mount is fully healed for an emergency getaway)
I found one in the back of Herbivore Island (I live there just so you know) and I KO’d it with a crossbow (NOTE: it was a level 4 and I have stuff boosted) and I was happy, but then the sarco I was on killed said mosa