The best way I found to tame these magestic creatures is buy building a cage on a quetz. To build said cage you would need a 2 x 3 use door frames. The way this cage works is you would need a quetz that is just barely faster then one. Once you have that all you do is move the quetz to where the tapejara would be in the cage and completely stop. This part is very important because if you move the quetz while it's in there it will just phase through. But after you stop the tapejara all you have to do is use your prefers method of knocking it out.
If ur tryin to tame one of these try lookin for them somewhere near the red wood-swamp border thts where they spawn... They're found almost everywhere around tht corner and try searching for them near the canopy, and another thing... If u suffer constant crashes and crash loops in the redwood biome then try to KO it asap then try to fly as high any can thtl unrender the rocks and other stuff then as soon any get the success notification get the hell outta there., recommended : high lvl Petra or argy
ARRRRRRRGH I just had THE WORST taming experience! Pro tip: DON'T try taming a high level one by dangling from an argy by a grappling hook... You'll end up dying TWICE and losing your argy, guns, and 80 narcotics... >:( :(