If tou wanna tame these easily on official I suggest getting Snow Owl(It can be low level) after you got that go to ragnarok build taming pen with 3 dino gates and knock it. While its knocked use snow owl to heal griffin. After its fully healed wait till it wakes up. After it wakes up knock it and heal it.[This way you will save narcotics] (Do this over and over till its food is low)
I recommend using a trap (unless you already have a grif then you can just tranq it in the air). I found that 7 dinosaur gates worked the best. Also I found it easier to have a friend on so they can lead it towards you in the trap. And then you just have to agro it somehow. Also make sure your tames are on passive in case it hits you.