To find a shiny, the chain must be at at least 40, although you can find it earlier through extremely rare occurrences. Keep the chain going by KOing the pokemon, so it is recommended that you have a high-level poke with a lot of PP.
To make it easier, use Repels, preferably Max, as they will make you only encounter Pokerader Pokemon...or any wandering legendaries that may be in the area. If you're going for a particular nature, have your lead Pokemon have the ability Synchronize, as it has a 50% chance to pass that nature to the enemy Pokemon. If you want a specific Gender, have a pokemon with Cute Charm in the lead, as it will attract pokemon of the opposite gender more easily.