Black Kyurem is the new mascot version of Kyurem that you can catch in Pokemon Black version 2 on the Nintendo DS.
This new Black Kyurem is Pokemon Black version 2 specific, and can’t be caught in Pokemon White version 2, which contains White Kyurem instead.
To catch Black Kyurem in Pokemon Black version 2, you first need to get near the end of the game and get the Zekrom from beating N in Dragonspiral Tower.
Once you have Zekrom, head to Giant Chasm north of Route 13, between Route 22 and Route 23.
Deep inside of Giant Chasm, you’ll encounter Kyurem. If you’re able to catch Kyurem, a DNA Splicer will drop to the ground which you’ll want to pick up.
You can use the DNA Splicer to combine Zekrom and Kyurem into Black Kyurem.
If you knock out Kyurem instead of catching it, you’ll have to beat the Elite Four to make it spawn again.