To solo tame, get a fast argentavis and a scorpion. Then put the scorpion on Aggressive and pick it up with the argy. Find a low level quetz and let the scorpion stab it. After you knock out and tame that quetz make it into a quetzal catcher to get a higher level one.
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.