Easy way : Bring a harpoon gun with net ammo and BASICALLY Shot the quetzal and make sure it falls in a safe area and then trap it as fast as you can and Tranq it with your ammo of choice and Normal Gates can work and even if it wakes up it shouldn’t be able to escape easily and to net it again you have to De-agro it
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.
I know this is pretty common knowledge, but for the guys who always find the quetzal they're trying to tame in an area loaded with sabertooths, carnos, and rexes, all quetzals that are frightened will fly towards the coordinates 50, 50, every single time.