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.

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