Near where you find Griffins, there's 3 huge water falls. Behind the middle one, there's a cave. I just lead griffins in there so they can't escape and tame them there. It's also pretty close to Scotland so can get Mutton for it easily.
i’m a lazy guy, and i don’t usually use traps when i tame things, other than BIG things like a reaper queen or a giga, but THIS IS THE EXCEPTION. unless your dad is apollo, it is impossible to knock one of these guys out without using a trap, for my case anyway. they are ridiculously fast, and they will circle you and attack you. however, the griffin is worth the trouble. it’s one of the fastest fliers, does devastating damage compared to other fliers, other than your typical high-level argy, doesnt need a saddle to ride, can fit two people, and not to mention it looks amazing. however, it can’t pick up many things, it can only pick up smaller creatures. if you carry cryopods around with you though, this shouldn’t be a problem. up this if you found this helpful! -J