Place a pachyrhino on top of a quetz saddle and approach the flying Tapejara, press C to anger it and then get off and shoot the Tapejara. Make sure you get back on the Pachyrhino and right click to stop it from being attacked. Fly off slowly and the Tapejara will follow you to where you want to go making it easy to shoot.
Go to extinction into the city area. Bola the Tapejara. Place stone gates around five or four stone gates with gateways with just small gaps in between the gate. You place this down fast. You can tranq it or club it.
If you are going to try tame one get a gille suit on sneak up behind it and bola it if you don’t have a longneck you can use whatever weapon you want and if you want a longer lasting bola use the chain one!