A wild Griffin is a damn dangerous flying monster.
It's fast, does a lot of damage, it' even flying around you like a vulture to make some psychological warfare. It has a dive ability too. Be aware that it is hard to tame it without any trap, but I've got you covered, just use a Netgun and it will instantly fall to ground, then you build 4-5 Gate frames on the Griffin while you have 2 Gates ready to close the entrances, so it stays put. Or have the gates built beforehand, lure it in and then close the gates.
Aaaaand... don't get hit, this thing can slay you and your whole family tree in a matter of seconds.
Once you have tamed it with some meat, prime meat, mutton, or kibble, you can get rid of your trap and mount this Demon without enslaving it with a saddle. It has 2 Seats, stays in air like a helicopter, you can even fly backwards or left and right. In other words: It's maneuverability is extreme. It has a nice Dive ability. The best and fastest way to move this thing is by diving all the time. Fly down until it reaches a nice speed and then pull it back up, with this technique, you are able to cross large distances in a short amount of time. It's able to pick dinos up, but only the small boys n girls.
It's one of the fastest and most dangerous flyiers by the way. You can even breed those Insane and awkwardly beautiful Bird like creatures.