Just use a Griffin and follow it around tranqing it, i just tamed a 180 tek quetz and it fell asleep on a perfect mountain!
Oh also bring far more then what dododex says, it told me I had more then enough tranqs but it still didn't go down
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.