Lead on down from the mountains into a trap. That trap is a bunch of Dino gates lined up with one person on the ground. Only put actual gates on the end gates. Fly through have the ground person close the gate behind you then close the other gate. Then when it is trapped tranqu it. Hope this helped
An argentavis can't fit through a ceiling with one tile missing, but a pteranadon or lymantria can. Build a trap with one corner ceiling missing, aggro the argentavis, fly in one side and out the missing ceiling tile, and land. Dismount, run around, and close the entry door. Tame safely at your leisure.