You have to go find Kyruem; after you beat Ghestis. You should lower Kyruem's HP before capturing. You should have a Master Ball, that would be the best way.
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Of course you can 2nd answer: the only nonunova legendaries you can catch are heatran, latias (white 2), and latios (black 2). You need to make black kyurem (black 2) but white kyurem (white 2) can't be traded. However, if you don't have black kyurem, you can make white kyruem, but only if you've caught kyruem.
Black and White Kyruem.
You catch Kyurem at Giant Chasm At the top right corner of the map on white or black
No. If you make it faint, then you can find it later
Kyruem is pretty hard to catch unless you didn't use your Master ball to catch Zekrom, I caught Zekrom with a Quick ball.