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. Help this get to the top!
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.
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.