All you need is 4 foundations on a quetzal platform, 8 fence foundations, and 4 Dino gates (no doors) fly into the quetzal and dismount this will catch the wild quetzal if it's between the gates then just tranq and tame. Give it's long tame time be sure if you are going to have to move your quetzal then there's a safe area below and wall it in with thatch or wood walls to keep predators away from it. Or if you got time to sit around just stay in the air for low level ones.
If you don't have another quetzal to lend a hand then just use any bird and either have a buddy carry you while you shoot it down or run it into a mountain side as they get stuck easily. If it falls and is still on the mountain then have some pillars and make a makeshift landing pad off the mountain side so you can fit an argie or something on it to keep giving it narcs.
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 drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.