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
For my first Quetzal, I was on my Pteradon and had my friend being carried with a crossbow with tranquilizer darts. I had to chase it for a good 20-40 minutes. He had to get the perfect angle. Probably isn't the most effective way,but still works. When we found another that was Tek, we used our Quetzal to follow it around and shot it with tranquilizer darts. It worked a lot faster.
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.
Be careful taming these, they have a glitch that makes them go to coordinates 50 50 when high torpor,
50 50 on the island is the redwoods,
50 50 on Ragnarok is murdersnow,
50 50 on the center I'm not totally sure,
50 50 on velguero is in the lake I think,
And 50 50 on extinction is the safest, in sanctuary city.
The best thing to do is 1. Get a arge, 2. Fill it up with stone or another heavy thing, until its ALMOST over-encumbered (aka so its slower when you grapple but not to slow. Now grapple onto that sucka and whistle attack target. Happy taming :)