If taming solo, use grappling hooks, parachutes if necessary, tranqs, and a bird. Grapple to the bird high up in the air and have a spyglass and whistle attack this target, when close whistle passive then shoot. Repeat
The Quetzal is a behemoth of a creature with base stats that top the charts (health, stamina, weight, and torpor). The Quetzal's platform saddle make it an excellent choice for a mobile air base or even a caravan for transporting and gathering metal and other supplies on harder to reach areas. While its melee strength isn't as high as some might expect, its health and ability to carry weapons make it suitable to use as a war bird. Its preference for Rex Kibble make it difficult to tame, and even more so difficult to knock out in the air. — Smallfoot
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.