If you're having trouble finding one, get on your bird and go to about halfway up a redwood tree. They like to climb trees and then glide from tree to tree so your chances of finding one in the trees are a lot greater. I found a group of five once in the trees. However, they will glitch when being grabbed from a tree. It might not always be in your birds talons... Anyway, if on the ground, bola it (without scaring it away like a tapejara) and tranq it. It has a low health pool though, so try to watch your arrows.
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.)
Found in the redwood forest biome mostly on The Island, can be seen majority of the time flying from tree to tree. Best tactic to taking is a decent longneck rifle and tranq darts. Shoot them after they have landed on a tree as they rest for a moment before moving again giving perfect window of opportunity. The redwood can be dangerous so bring a means of defense like spiked wall
The Archeopterx.....ah.....one of the newer additions to Ark. I find them to be a very fast creature(I'd use a Bola to tame them), and a useful one at that.
Worth its time limit for tame. And remember one thing, not that easy to find.
However, It's easier to find in Scorched Earth than the normal one.