In order to catch Zygarde, you must first complete the Island Challenge and defeat the Elite Four.
Zygarde can be found in Resolution Cave, which is located on Poni Island. Use Charizard Glide or the Machamp Shove ability to navigate through the cave.
Once you reach the end of Resolution Cave, you will encounter Zygarde. Battle it and use Ultra Balls or Dusk Balls to increase your chances of catching it.
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