If you have a Quetzal, put a simple cage on it (This cage worked for me https://youtu.be/oHx1KeJX408) and have it follow your Argy, check every once in a while it doesn't get too far. Land your Argy on Quetz to regain stamina. Quetz will never run out of Stamina.
When you find your wild Quetz get in your Quetz and have Argy follow you and not your Quetz in case you fall. Always carry lots of parachutes in case you fall.
Get wild Quetz stuck in cage and take it down. When your Quetz gets low in stamina, jump on your Argy and let it regain to full. Repeat process until done. You can also check stamina of your Quetz will flying your Argy and getting close to your Quetz. No meat and stimz required.
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.
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.
Kind of a long process but worth it.
Tame a griffin, shoot tranqs from griffin, knock Quetzal.
Tame Quetz and put all points into Stamina. Make trap on platform made of thatch. Lead the wild Quetz on the trap you made and just chill mid air as you knock and starve the wild Quetz. EZ PZ cause that’s what I’m doing as I type this.