Details: Outside of the Cover Legend, the next Legendary Pokemon you will encounter is the Melemele Island Guardian Tapu Koko - there is no doubt about this. After defeating the Elite Four, during the Festival back in Iki Town, you and Lille will break away to the Ruins of Conflict. After she gives thanks and you do the same, Tapu Koko will appear and you will go into Battle with it.
Tapu Koko will be at Level 60, knowing the Moves of Nature's Madness, Discharge, Agility and Electro Ball. It is an Electric/Fairy Type Pokemon. It has the ability of Electric Surge, which creates an Electric Terrain within the Battle. With this type of terrain, the powers of Electric Moves increase by 50%. Pokemon on the ground will also not be able to fall asleep.
Since Tapu Koko is a stationary Legendary Pokemon, it can be battled again if a player were to run or accidentally defeat it. However, the player will have to defeat the Elite Four again before Tapu Koko reappears.