I used a tapejara to tame a quetzal solo. I added enough stone into my inventory to slow my ride, then hopped in the front seat with a tranq rifle and whistled my tapejara to attack the quetzal. Since it was slowed down, it wasn't able to get close enough to the quetzal to attack it after I started firing. When the quetzal was getting too far away, I dropped some rocks to speed up. It was overall a somewhat tedious process, but in the end it was worth it.
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.
Three stepped method of how to tame a high level quetzal on mobile solo:
1. Tame a tapejara and pump its speed
2. Fly up to a quetzal (preferably low level female) on your tapejara, get on the passenger seat, whistle your tapejara to attack the quetzal and start tranqing. Whistle passive if your tapejara gets too close. When the quetzal goes down, quickly secure the area. You can use spiked walls. Once you get your first quetzal, pump speed, stamina, and maybe weight.
3. Kill every quetzal you see until a high level one spawns. Put a platform saddle on your low lvl quetzal, build a 3x3x3 box on its back with one side opened. Fly ahead of the high lvl quetzal and wait for it to enter the box. Then build walls/doorframe to complete the box and now you have a trapped high lvl quetzal and you can tranq it. However, once knocked out, the quetzal will most likely glitch through and fall to the ground, so make sure you avoid trapping quetzals over dangerous areas or water.
The easiest, EASIEST way to tame a Quetzal, is to go to a GEN 2 server, fly up to it yourself, shoot a net at it fall to the ground with and hit with tranq darts. Wash rinse repeat until ready to tame, then it's all down hill from there, unless there's a predator near by. Regardless of what you do, you need to prep before hand, bring a lit of Narco, tranq darts and food (dealers choice/ refer to doddex). Then it's all yours.