The longest way to tame a quetzal✨, first get 100 amber, and then find a griffins at the north west mountain in the island, pick a high level griffin, buy a change name card using 100 amber, and then use that change name card to change your name with the griffin you want to tame with its initial ( i cant explain it any better, just search it up in yt ) and then once it gains respect to you, lour it to your trap, and the give it narcotics after knocking it down, and then go to the south cave and get the artifact, and now tribute it to any obelisk and you'll have a chance for a 10× soothing balm, and then put raw prime meat in the griffin and the soothing balm, and once its tamed, go get rifle with tranc dart, and then knock down the quetzal while riding the griffin, you're welcome.
The fun way is to jump off and grapple to your argie and whistle it to attack and since argies are slow it won’t catch up in time so tranq till it goes out also bring parachutes and consider liking so more people will know
If you manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.