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
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.