They're pretty easy to take.

Get an underwater tame. I highly recommend the Basilosaurus, as the jellyfish + squid + eels can't knock you off or stun you.

Head to the underwater trenches and reefs near the far left side of the Fjordur map, turtles will be everywhere.

If possible, get a Tek Helmet and activate the sonar down there near the ocean floor. This will detect a school of fish for you.

When you find one, agro them and lead them to your Meacheron. They'll de-agro on you and begin following the turtle, and this will start your tame.

(Be sure to protect them from Megalodon, Ichty and Coecalanth)

More Megachelon Taming & KO Tips