By far, the easiest method (in my experience) for taming one of these little guys is this:
Beforehand, prepare about 50 narcotics, as it doesn't take too long to tame a lvl 150. You'll need either chitin or Pelagornis kibble. I would just use chitin since you only need about 80 or so for a lvl 150. Next, you'll want to have a bola. I would craft at least 3 in case you miss. Once it's tied up, go ahead and tranq it with tranq arrows or darts. You shouldn't need more than 20 tranqs. That's taking into account how often you may miss. But since it's tied up, you'll have far more than you need afterwards. I suggest letting it starve all the way down, and then putting in the chitin. That way your resources arent vulnerable until the last second. Wait a little bit, and you should have a lvl 150 Archa. Enjoy :) (Lower levels follow the same method with less resources, I simply used 150 as the example.)
I see the Otter God, the Jerboa King and the Defender of Bulbdogs made an early move. Now I the Archaeopteryx Lord shall rise. If any one of you guys kill these birbs I will look for you and feed your soul to the ravenous birbs I own. So if you see one my birbs Naruto running away for you, DO NOT kill it instead be its friend, they are a great parachute and they are wholesome creatures to begin with. So you have be warned by the Archaeopteryx Lord...
They are very fast and will only eat chitin. They run away when they see you or you tranq them. Breeding takes chitin too so have lots of chitin. They hide in trees and I have only seen females so Esther males are rare or I’m very bad at finding them
On mobile these guys tend to glitch out a lot, so try to shoot them when there completely still on a tree. When glitching they often just teleport tree to tree and/or slowly slide down the tree until they fall to the floor (from my experience you cannot hurt or knock them out in this state)