These guys are some of the best tames in ark because you can tame things from its back by running away and tranqing your target from its back.

To tame them fly around in the red woods with a flyer that is on passive flee until a thyla tackles you out of the air. You need around 300-500 health and flak armour to survive the attack. Once it tackles you shoot it with a net gun if it's high level or just start tranqing it mid air and chase it (you need about 160% movement speed to catch it again)

Disclaimer: Make sure your flyer will not kill your thyla, I have lost 3 thylas that way.