So you want to catch Kyurem, once and for all? Guess where it's chillin'? Back in the Giant Chasm , where you battled it after chasing Ghetsis! You need to have first captured Zekrom or Reshiram first from Dragonspiral Tower . Once you have, it's off to the Giant Chasm you go!
Either get there by Flying to Humilau City and heading through Route 22 into Giant Chasm or, if you pushed that boulder into the hole when exploring Giant Chasm , Fly to Lacunosa Town and head east into Route 13 . Near the start of the route you'll see a boulder in a hole.
Move over it and head north to the entrance to the Chasm. Head inside. If you entered by Route 22 , you'll need to head south, then west until you see a large set of stairs leading down to a doorway. If you enter by Route 13 , you'll start nearby this doorway. Head down and enter it.
You'll be out in the forest area where the Plasma Frigate was. Head down the stairs and head north. When you see some Tall Grass leading east, follow it. You'll appear in the clearing that the Frigate created. Make your way to the east side of the clearing.
Then head north-east through a gap, some Tall Grass then some Dark Grass. Head east to the very edge of the area, up against a rock wall. Now head north along the side. When the path turns west, follow it up until you reach the stairs leading up to a cave. Move up them and enter.
Head through this area of the cave to the doorway at the end and enter. Move through until you reach Kyurem . If you want to catch it (and why wouldn't you?), Save your game before you start the battle.
That way you can restart if you accidentally make it faint, or if it 'accidentally' utterly owns your team. If you do defeat it though, you can always make it through the Elite Four once more and it will reappear, but it's not recommended.
Legendary Pokemon Battle
Once it's over, Bianca and Cheren will come in to chill and have a relaxing chat with you. After conversing for a while, they'll leave. Pick up the nearby item, the DNA Splicers . You can use this to fuse Kyurem with Zekrom or Reshiram to obtain Black Kyurem or White Kyurem !
Now head back outside and Fly to wherever you'd like and do whatever you'd like! You're now free to do whatever Post-Game content that you want! You can also head into Twist Mountain from Icirrus City, but it's recommended you access it from Clay Tunnel instead.
As well as that, there's eastern and south-eastern Unova to explore. If you wish to explore eastern Unova, see the Back At Undella Town section. If you wish to explore south-east Unova, see the Skyarrow Bridge section. Or check anything else that takes your fancy!