(MOBILE) My way how I tamed a quetzal is:

I found a quetzal arround the green obelisk

Then I killed it with my argy (don't harvest quetzal)

Then took his implant from him

Placed revival platform and built thatch things arround, so he cant escape

Then I knocked with tranq.

You can bring ur friend so he can help u tame it, with Tapejara, Argentavis, Pteranodon,

With Tapejara, ur friend controls Tapejara and you sit on the back and knock out the quetzal

With Argentavis, your friend picks you up with Argentavis and then he flies to Quetzal and you try to knock it

With Pteranodon, same like with Argentavis

-Hope this helped.