the royal griffin can be found in fars peak here's a method to tame a royal griffin

1. Have 4 stone dinosaur gateway(or more)

2. Have 2 reinforced dinosaur gate(to make a trap for the griffin so it doesn't escape)

3. Have a flyer

4. Lure the royal griffin into the trap

5. If the royal griffin is trapped close the gate

6. put spike walls around the trap so no creature can interfere your taming

7. Proceed to tranquilize it

8. If knocked out put it's preferred food into its inventory(allosaurus kibble can work)

9. Bring narcotics

10. If you have enough ancient amber to buy soothing balm(which cost 40 ancient amber for the 15x soothing balm) buy it because it could take a long time to tame it without soothing balm