My guide to catching legendary Pokemon
This is usually how I capture mostly all of my legendaries;
Step 1: Go for the Legendary at night.
You will need:
10 Quick Balls
10 Dusk Balls
10 Timer Balls
Approximately 40 Pokeballs
Pokémon with False Swipe
Step 2: Okay, so once you have those things, save once you are in the same room as the Legendary (in this case Zygarde).
Step 3: First, use a Quick Ball. If this fails, proceed to step 4.
Step 4: Use the second Pokeball in your arsenal. The Dusk Ball. If this fails as well, proceed to step 5.
Step 5: Using one of your Pokémon, decrease its HP to a bit less than half or to the red zone.
It may help if you inflict it with sleep, paralysis, or freeze. Burn and Poison aren't that good, as they can faint it.
Step 6: Start spamming Pokeballs. Believe it or not, I caught a few legendaries this way. Then you could show your friends how you caught your legendaries with Pokeballs.
If this didn't work after 10 Pokeballs, proceed to step 7.
Step 7: After the 10th Pokeball, use a Timer Ball. If this still fails, repeat Step 6 and 7 until you run out of Timer and Pokeballs.
Step 8 (optional): If you still don't capture it (which is unlikely) , start spamming all of the Pokeballs you have, and do anything it takes to capture it.
Step 9: If all else fails, restart the game without saving, and restock with double all of the items.
*If you accidentally kill the Pokémon, quit the game without saving, then play the game again to your old save point.
Hopefully this will help you capture the Pokémon!
Edit: The title is catching legendaries, not hatching legendaries. XD Sorry, I was doing my Honedge shiny hunt at that time.