An effective way to knock the Tapejara is to wait for it to land, equip a bola then run straight at it while swinging the bola, as soon as it does it's 'roar' then throw the bola at it before it flies away. If you don't bola it in time it will fly away very fast, if you get it out of your render distance then load it back in, it will have stopped flying away and be in a normal state, ready for you to try again.
They are skittish but not anywhere near faster than humans. They have low torpor and health, so tranq darts are recommended. Tamed like any carnivore, kibble is Archeopteryx. Can be found anywhere in and around the swamps.