To solo tame, grapple to an argentavis, and be ready to set your argentavis to passive and attack my target on command. Just maintain a process of having your argentavis chase the quetzal, when you get close enough set it passive, then fire a tranq dart/arrow. This is a long process, but it is by far the easiest way to solo tame, unless you already have a quetzal.
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.