If you are willing to tame an Argentavis do not keep on shooting it with darts or tranqs otherwise it will die. So shoot it and wait about 5 seconds before shooting it again to prevent it from dying. Do not tame an Argentavis on Carnivore Island as it will get eaten.
To tame one easy all you have to do is kill something so the argent Avis can eat, and while it’s healing you must knock it out with tranq arrows or darts. If it is knocked out while healing it’ll starve immediately and it’ll tame in seconds no matter what level!
If you lose your argys go to the place that shows your character press the tames button which says how much animals you have, Look for your argys name press request, then wait. It will tp to you, if it’s alive.