If you want to tame a Quetzal, and you don't have any paracute or grappling hook, just shoot it with a shocking tranquilized dart (recomended) on your Griffin. Make sure that you shoot it in it face or butt. And don't forget to bring some metal spike wall (recomended) if the Quetzal knocked in the dangerous area.
If you have any dodo arrows, make a trap (tutorials on YouTube) the shoot the quetzal with the dodo arrows. The quetzal will get triggered at you and lead it to the trap. Up vot so dododex can see this
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.