Get a high level pteranodon lure it on top of that big mountain with a crater an keep it in the middle and knock it out. Since you have a high level pteranodon you can fly around and kill argentavises for easy prime meat.
If you need an argy and don’t have time to tame one with a trap, just go to carno island, kill a Dino in front of an argy and let it harvest its body. When the green health icon shows up on top of it, knock it out with tranq arrows and the argy is instantly yours.
Just finished my first tame with 10-12 tranqs to the head. My mesopithecus came in super clutch, poo throws really helped me kite and allowed for super easy headshots. Used about five narcotics to keep him down.
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.