Dododex tells you the amount of traqs to knock the quetzal out. But it doesn't tell you that the bird's torpor recovers quickly and it will take more traqs the slower you hit it. To knock the queztal out with the least amount of arrows is to hit it quickly as it trying to fly away. Don't wait for it to slow down.
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.