Get a basilosaurus and get the manta you want to tame, agro it to the balsilo and you will be able to tame the manta since its attacking the basilo instead of you. (The basilos food will drain quickly so get it some food)
Just pump health and when I mean pump health I mean PUMP THAT HEALTH! These guys die so quickly. I know it says on stats they have 320 health at level 1 but seriously they are so STUPID! in the wild, they sometimes jump in the middle of the most unuasual time and they instantly die even if the Manta is level 999 and even if its tamed it will only take MAXIMUM 9 seconds to die on land. AND ALSO IN BATTLES I DONT KNOW WHY BUT IT FEELS LIKE THEY HAVE HEALTH DEBUFF cause apparently they die so quick, especially to megalodons. Weird...
So just pump health.
When taming place a stone foundations with doorframes on all sides except for one in the water with doorframes just under the water, aggro the manta in the spot and place a doorframe to lock it in. You can feed it while it aggro to a wall for safe taming.
Never I mean never bring your high level Rex in the water in the center map because like 20 of these things killed my level 171 Rex after I tamed it and was going to lava island and my Rex fell off the boat.