You will need:

3 dodo arrows (to Argo it on you)

500 biotoxin (if taming without balm) and 100 if using a balm.

4 dinosaur gates

A lot of raw meat

About 100 tranq arrows

First of all, set up 3 dinosaur gates in a square shape.

Now, find your quetzal, and hit it with 1 dodo arrow until it chases you. When it starts to chase you, quickly lead your quetzal to the trap and trap it. As soon as your quetzal is trapped, put the last dinosaur gate right behind the quetzal, to stop it from moving quickly. Now, knock it out.