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)
Tame a kaprosuchos and swim to one of these bad boys and do it's alternate attack it will grab it in it's mouth. walk onto the shore where its safe and have another person feed it while in the gators mouth (if you unmount it drops it) it wont attack or die because it's technically not on the shore.
They have terrible turning circle, approach one from above and feed it. Then let it swim circles around you. The occasional time it gets close you can predict its attacks, it “bucks” just before the attack, which is the tail swinging underneath. Quick swim up or back avoids it. Be prepared to get dizzy, long time between feeding
I’ve found the best way to deal with these guys is using a Pelegornis in shallow water. You’re able to hop off the water, fly, and still follow the manta around. It’s easy to hop back on the bird if you land in the water so it makes it easy for a quick feed and then retreat.