First earn the Royal Griffin’s respect through the appropriate character requirement, matching surname, or crown, then lure it into a secure stone trap and knock it out with a rifle and tranquilizing darts. Apply soothing balm and feed it its preferred kibble, keeping plenty of torpor-maintaining narcotics or biotoxin on hand while staying nearby until the tame is complete. If breeding one, protect the slow-growing baby in a secure shelter until it can fly.