I would recommend Consecutive Fishing! This is where you fish for a shiny by standing in one spot and not making any movements. To succeed in this you must achieve a +40 chain without getting "nothing seems to be biting", going to the menu, or moving. To ensure a bite catch a Suction Cups or Sticky Hold Pokemon with these abilities.
So far I've Caught a Shiny: Skrelp, Relicanth, Horsea, and Shellder
It takes patience :)
Hope I Helped.