Knocking Out: To knock out a Quetz, best idea you can do is be carried by a Argie, people say Ptera but I prefer not since it's feet can easily be shot by the arrow, and keep on targeting the head. Remember to put speed up for Argie as the Quetz have a decent speed on their hands. You can also use another Quetz with a platform, but this is only if you do not own another 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.