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.
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
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.
Use a netgun when it flies above ground. Once netted, either have a trap ready for high levels or shoot tranq arrows into their eyes(more dmg). It you have a buddy, have them shoot with tranq darts while you shoot into the eyes with arrows. Be careful though as they’re kinda wimpy at times. Super hard to tame while solo without a net gun.
You can net a quetzal but before you do clear the area of any hazards and hop on you creature and bet it (Make sure you don’t shoot it when it is asleep because when is has the bet on it looks like it’s asleep)
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.