Have one of your tribe members pick you or another person up while holding a crossbow/rifle then simple have the flyer fly over the quetzal and shoot at it till KO'ed

If your alone do the same thing except use a grappling hook and connect to your flyer of choice and whistle the flyer to attack my target while aiming at the quetzal and whistle stop all when in shooting distance of the quetzal

More Quetzal Taming & KO Tips