When trying to tame a quetzal it is hard to do it alone so grab a small amount of gear like a bow with tranq arrows and fly over it. After flying over it try and drop on it. ( this might take a few try's) once getting on the back shoot it with your tranq arrows. This will allow u to tame it if your alone. ( this method is hard)
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 drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.