Build a quetz trap with a single foundation in the center of platforms saddle. Then put 3 ceilings on the sides then a hatch frame on front of platform saslddle to be able to mount and dismount easier when in air. Then 3 door frames up on the ceiling tiles leaving the front open. Place four ceiling tiles at top to close top off. Find a quetz fly head on at it and once it's in hop off quetz and place 3 door frames at front side to trap it. Now tranq away. Easy air tame. No threats
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
In order to solo tame a quetz, you could use an argentavis and a pulmiscorpius. Just pick up the pulmiscorpius, and do whistle attack target while looking at the quetz, your pulmiscorpius should start attacking the quetz, raising it's torpidity until it is knocked out.