When taming Griffins I always use my high level Argy, he has nearly 20k health and I set him to passive and let the Griffin bite him as I shoot it, or I let the Griffin bite me because although they have decent damage, flak armour and 800 health seem enough to survive,
It should take about 46 regular darts to get a level 60 to fleeing amount of torpor including inaccurate shots, after that about 9 more for it to go to sleep, I'd recommend first taming the lowest level you can find and then using it to
tame higher levels later, if you want a high level Griffin without taming worse ones first, a trap would be necessary,
I haven't tested it yet, but building an octagonal amphitheatre/coliseum shaped trap of wood or above to delay it's escape with slightly over hanging walls so it doesn't fly away when it flees would probably do, after it goes to sleep normal meat should tame it after a while, but be prepared to lose a lot of narcoberries/toxin/narcotics
In mobile, if your names last two letter and griffins last two letter is same they respect you and in mobile i knocked out it but he didnt eat the meat you must use allo kibble or griffin kibble. (please click up button for everyone see)
If you do not have a trap definitely make sure you have a tame that can soak hits while still being able to pull out a weapon on the tame, I reccomend a thylacoleo if you are attempting this method but I strongly advise people to use a trap, I reccomend a trap that is 5 dino gateways long with gaps only humans and smaller creatures can fit through along with dino gates on the end dino gateways!