Anytime after defeating the Elite Four and the main storyline, you can Battle Tapu Fini, the Island Guardian of Poni, at the end of the Ruins of Hope. Like all the other Lake Guardians, it will also be at Level 60. It's ability instantly creates a Misty Terrain, which reduces Dragon Type Moves by 50% and prevents status conditioning.
Tips For Catching Tapu Fini:
Thankfully, unlike Tapu Koko, Tapu Fini actually can be paralyzed, just not until the Misty Terrain has been removed after five turns. This makes it much easier to catch and almost ensures your Pokemon will always move first. After finally paralyzing Tapu Fini, and even in the meantime, try to get it's HP as low as possible. Water Type Pokemon are best against Fini, especially since its move don't do that much damage to them. Having False Swipe and Hold Back on some of your Pokemon also helps, since it will guarantee Tapu Fini is left with at least one HP.
From there, after getting its HP as low as you think you can, Ultra Balls are the best way to capturing it. It will usually take a lot of them to catch this Legendary Pokemon, but they are still your best option. And don't forget to save before battling Tapu Fini, just in case you are going for a certain ability or accidentally knock it out.