To solo tame first build a 6x6 trap at the tribute terminal(obelisk) make it 4 wall high use door frames. Then use a flying dino and bring 2 pteranodon with you, then hunt one if you found one order your pteranodon to kill it make sure to turn off their loot victim so the dead quetzal doesn't disappear, if they kill it take its life artifact and bring it to the tribute terminal and it should be trapped in there and knock it out and tame
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.
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 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.