These things are only available on the Mobile version, they spawn at the mountain near Carno Island (along with Gigas so be careful), they all have their own names, and your own name needs to end with the same letters of the Griffin's name for it to respect you, or be Level 95 and all of them will respect you (or buy the premium crown), they take a LOT of prime meat to tame, don't ever try taming one without a soothing balm, even a low level could take hundreds if not thousands of prime meat. They prefer their own kibble so tame a low level breeding pair before taming a high level one with Griffin kibble.

More Royal Griffin Taming & KO Tips