If you have a tapajera with a three person saddle you can hop on the tapa fly it around until you find a quetzal and shift to the front seat tell your tapajera to "move to" the quetzal and when it gets close enough shoot the quetzal with a tranquilizer dart and repeat until it crashes. Works better with two or three people so you can line up shots for the passengers.
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 manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.