When knocking out your first Quetzal it is best that you have a army with good stamina and good movement speed to keep up with the Quetzal. Always remember that the redwood is the worst place to let it fly into because it could get lost or despawn.
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.