Instructions
Run around in the long grass. The more encounters you have, the greater the chance of any one of them being shiny.
Add a Pokemon with the Illuminate ability to the front of your party. This ability attracts wild Pokemon.
Ride your bike when shiny hunting. This allows you to cover more ground, which causes more random encounters.
Save your game just before fixed encounters. If the Pokemon isn't shiny, just reload and try the encounter again.
Breed shiny Pokemon by saving right before you take the Pokemon egg. Since shiny status is determined when you take the egg and not when it hatches, do not save your game until the egg hatches. If it does not hatch a shiny Pokemon, reset the game and take the egg again.