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
For some reason on Ark Mobile, it does not allow me to shoot off an Argentavis when grappled. I think that is a bug on my phone. Anyways, I found the easiest way to get a Quetzal is to ride a Tapejara with multiple seats on the saddle, and then go to second seat. When you do this, shoot the Quetzal and use the spy glass to target him. If you keep shooting the Quetzal while it runs, you should not have to whistle passive for your Tapejara. Then, grab some meat and a lot of bio toxin. Boom, you have your new Quetzal.
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.
If you manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.
If you want to tame one set a tamed Tapejara to follow you but you have to be off your tame first then find change seats a quetzal set it to attack the quetzal and shoot some tranqs and you can set your Tapejara to follow you when you are of it and when you fly it it will stay in the air so it is a easy way to kill alpha’s.
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.
To solo tame, grapple to an argentavis, and be ready to set your argentavis to passive and attack my target on command. Just maintain a process of having your argentavis chase the quetzal, when you get close enough set it passive, then fire a tranq dart/arrow. This is a long process, but it is by far the easiest way to solo tame, unless you already have a quetzal.
Kind of a long process but worth it.
Tame a griffin, shoot tranqs from griffin, knock Quetzal.
Tame Quetz and put all points into Stamina. Make trap on platform made of thatch. Lead the wild Quetz on the trap you made and just chill mid air as you knock and starve the wild Quetz. EZ PZ cause that’s what I’m doing as I type this.