First if possible have someone on a server who already has a Quetzal(and a platform saddle) that will be willing to help you by building a box shape on the platform leaving the back open, next fly in front of the Quetzal having it fly into the box then put the back walls on completing the box and making it so the Quetzal is trapped, after that fly closer to the ground in a safer area and proceed to knock it out after it unconscious take the back walls off and have the person with the starting Quetzal fly forward let the Quetz to fall onto the ground so you can begin taming!
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.