If you feel you need to get closer, using ghillie armour will allow you to get closer than if you wear any other armor.
Bola it and once caught, then walk right up and use tranq darts or shocking tranq darts which is what I prefer (even though they require more materials to make). Took one shocker to the head for a low level.
Extremely difficult to tame. Best options are to bola it, and then use a longneck rifle with tranq darts. Otherwise trying to get it to fly into the side of a cliff and get stuff is the other option for a solo tame.
Since the new update, rare flowers make dinos aggro on to you, you can use this on a tapejara and it will follow you to a trap you've built. Just remember that each flower gives only 10 seconds of that debuff so if the bird is far away from your trap, you have to use it frequently while coming back. Also, if you need it to follow you after you've gotten off your dino, you need to eat another rare flower so that it can agro on to you once again.