Immediately after defeating Professor Kukui and the Elite Four, as you have a Festival back in Iki Town, you will ultimately be prompted to Battle Tapu Koko, the Island Guardian of Melemele Island. Tapu Koko is a very fast Pokemon, with offensive strengths that are no laughing matter. It's ability also creates an Electric Terrain, boosting all of its Electric Type Attacks and preventing sleeping.
Tips For Catching Tapu Koko:
Unfortunately, Tapu Koko is part Electric Type, which means it isn't possible to paralyze it. You also won't be able to put it asleep while there is an Electric Terrain, which basically means you'll have to catch Tapu Koko without inducing any type of Status Condition with it. And since it's at Level 60, this means it's going to be a tough capture.
However, outside of its Nature's Madness move that onnly cuts your Pokemon's HP in half, Tapu Koko only has Electric Type Attacks. If you have a few Ground Types on your team, this will definitely play to your advantage. Also having a Pokemon or two with False Swipe or Hold Back as attacks helps, since it will ensure Tapu Koko is left with at least one HP.
After lowering Tapu Koko's HP as much as you can and feel comfortable with, Ultra Balls are the way to go. They give you the best chance at capturing Tapu Koko, so make sure you have plenty BEFORE facing the Elite Four. And don't forget to save before and during facing the Elite Four, just in case you accidentally knock out Tapu Koko and don't particularly want to face the Elite Four again before being able to find it again.