I have tamed him with parachute,grappling hook and argentavis. I took my argent flew to the quetzal jumped off used parachute shot my argent with grappling hook command him to attack the quetzal a started shooting at him. I think this is one of the easiest ways to tame him
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.