If you have access to a snow owl, you can tame these with any crossbow! Just shoot it until it looks bloody, and heal it with the snow owl’s ability. Do it so that it heals quite a bit, but not so long that the torpor drains back empty. Then hop off the owl and continue shooting it with tranq arrows. I knocked a 140 with a 279 crossbow and using this method it had over half hp remaining once it finally went down.
Definetly top 3 Strongest fliers in the game so its a must have, Get a Pterandon (Or argy but there more valubale in my opinion so I use pterandon) and pick your tribesmate or the other way around and get it to chase you as you shoot it with good knockouts (shock tranqs) cus these things will kill you both or die first so be fast once you knock it out build a fence around it seeing as they are rare-ish so nothing kills it and if your on a pvp server protect this thing if on a beach or open feild chances are someone will end the things life.
Be very careful when near the griffin. It's very aggressive, and the fastest flyer in the game. If you're a low level with only stone tools, then run like the wind( Try to get into water ). However, it's an amazing tame, so I suggest you should get it.
People told me that if you encounter one they're very vicious and will attack you. In my experience, they are not at all like that. They only hurt you if you get too close to them as they fly around in circles really fast. But they never target you and attack.