Fly to Couriway Town . Head north into Route 18 - Vallee Etroite Way and hop on over to Terminus Cave from here. Enter it through the main entrance. If you haven't explored it yet, you might want to skip back to the section on Terminus Cave (Gym 8) and go through it before reading on. Once you're ready; continue reading.
Inside, follow the path to the next set of stairs leading down. From there head south to the ramp. When you reach the ramp, head west from it over to the ledges. Jump over the ledges. Now walk up the ramp to your west and follow the path across the bridge.
Once you're across the bridge head south until you move down a ramp. When you do, take the ramp leading up to your east. Head over the bridge, then loop around and walk down the ramp. Head north past the worker. When you see the stairs to your east head down them.
In the next area, head north past the Battle Girl. Keep going north, winding a little until you reach a Black Belt. When you do, head east from him. When you see a path leading south, take it. You'll walk past another Black Belt. Follow the path around until you reach two ramps, one to either side of you. Take the one leading up east.
You'll come upon a pair of Rangers. Head south past them, then follow the path until it splits into two paths, one leading east and one west. Take the path leading east and you'll reach stairs leading up. Take them. In this area, follow the path leading up north, up a few ramps. At the top you'll find another set of stairs. Head up them too.
In this area, head north. You'll come to a point where the path splits into six paths, including the one you just came from, the southern path. Head down the south-west path to find an Adamant Orb at the end. Head back to where the paths split and take the south-east path to find a Lustrous Orb at the end.
Head back and take the north-east path. At the end, use your Dowsing Machine to find a hidden Big Nugget . From there, go pack and take the north-western part. You'll find a Griseous Orb . Sweet! Now head back to where the paths split. Finally, take the path north.
You'll find Zygarde here! Time to take him on! Obviously, save the game before you battle it as you only get the one chance to catch it . If you end up failing, restart the game and try again until you do. Bring heaps of Ultra Balls or a Master Ball if you have it. Once you're ready, interact with it and the battle will begin!
Legendary Pokemon Battle
Obviously, you'll want to catch this guy - short of trading, you'll be lucky to find this Pokémon again. The sure-shot method would be to use the Master Ball . However, the Master Ball is a one-time item that you'll want to save for more annoying Pokémon that just have to run away from you. Or at least more powerful Pokémon.
The other way? Teach a Pokémon to use **** Stun Spore or Glare and False Swipe . Either of the first two moves can be used for Paralysis, which boosts catch rates. False Swipe is a 40-Power Normal move that won't kill. (If you can't use it, try moves that deal less damage than normal: it's riskier, though!)
You can try using False Swipe for two turns after Paralysis is induced to try and see how well the quadruple-rate Quick Ball will do on this fourth turn. If it fails, then just lower the Pokémon's HP to 1 and then begin shooting Ultra Balls at it.
Keep track of turns, though - after 20 turns pass, the Timer Balls will begin to be more effective. They have a x3.0 catch rate at that point (Ultra only is x2.0 ), but if you're low in number, you may want to wait some more until they're up to x4.0 later. Dusk Balls also work, since you're in a cavern.
(For the record, status-wise, Sleep and Frozen are 33% more effective to the catch rate than Paralysis . However; neither stat is permanent without curing, and no move causes Freezing without damaging the Pokémon.)
Once it's caught, quickly run back out of the cave. Now feel free to do whatever you want!