Extremely difficult to tame. Best options are to bola it, and then use a longneck rifle with tranq darts. Otherwise trying to get it to fly into the side of a cliff and get stuff is the other option for a solo tame.
Since the new update, rare flowers make dinos aggro on to you, you can use this on a tapejara and it will follow you to a trap you've built. Just remember that each flower gives only 10 seconds of that debuff so if the bird is far away from your trap, you have to use it frequently while coming back. Also, if you need it to follow you after you've gotten off your dino, you need to eat another rare flower so that it can agro on to you once again.
Look it is hard to knock them out because of the fact that if you get close to them they will run. So you are going have to hit a 360 bola trick shot with the bola and hit it then knock it out. One more thing whe you are shooting it with tranqs they have low health so wait 5 seconds to let the narc kick in. Have fun and good luck survivors!
Wear ghillie suit before approaching. Crouch/crawl up to then when it lands and use tranquilizer darts instead of arrows. Arrows have a very high kill chance. Once it goes down circle the tame with spike walls as tapejara are very fragile!
Probably the best flyer on The Ark, while I still think the Wyvern might be better on Scorched earth. Still, I love that you can hang upside down and on sheer cliffs. My absolute favorite flyer. ðŸ˜Š good luck out there!
After you manage to find one of these (usually high in the air, above quetzals. I've had the most luck around 50, 50) you'll want to make a trap. A Trapejara. Make a 3x3 cage out of doorways and put a ceiling on it.
Find your victim.
Fly level to it, using the back center doorway to line it up. Now for the chase, you'll want a quetzal with... a lot of movement speed. Mine is 211 and I struggle sometimes. Fly straight for the Tapejara, and once it clips into the structure, GET OFF OF THE QUETZAL. Your new buddy is trapped and afraid.
If you fail, let it fly out of render distance and try again. It won't be aggro'd anymore and it'll be flying normally do you have another shot.
If you just want to keep chasing it, wait about 15 seconds and it'll re-aggro, pausing for a second to do an animation. This is when I usually catch them.
A great taming mount with friends! Have one person drive and another shoot tranqs, makes tranqing flying creatures like argies and quetz a breeze, but you can also use this technique to tranq just about anything. Solo, you can hook onto walls such as cliff sides and try to fire from the saddle, although the angle tends to be difficult.
Otherwise, it makes a great "pick up" mount, use it to pick up friends that may have lost their flying mount or otherwise stranded themselves far from home.
However they are quite slow, consider putting a number of points in speed and a few in weight, especially if you want to keep up with fleeing quetz. With enough weight they can become an interesting alternative to an argy.