After defeating the Pokemon League, you and Hau will help the Ultra Recon Squad capture Stakataka in Poni Grove on Poni Island. Like all Ultra Beasts, Stakataka has some pretty incredible stats. It's more of a DefensiveType Pokemon, with extremely good stats in both its Attack and Defense.
You will always find and battle Stakataka at Level 60. The first thing you can do to try limit Stakataka is paralyze it with the move Thunder Wave, thus making it easier to capture. The main goal should then be to try to lower Stakataka's HP as low as you possibly can. A move like False Swipe works great when it has low HP, ensuring to leave it with at least one HP. The lower its HP, the better chance you have at catching it. If you have the Rotom Power that makes it easier to catch a Wild Pokemon, then you should definitely consider using it here as well.
But do make sure to keep track, as the more Pokemon Stakataka knocks out on your team, its Highest Stat will increase every time it does so because of its Beast Boost Ability. Because of this, like all the other Ultra Beasts, it's best to try to capture it as quickly as possible with Beast Balls, since they have a x5 Catch Rate when used on Ultra Beasts. And don't forget to ALWAYS save before trying to find Stakataka. It's a safety precaution, one that has worked since the first generation of Pokemon.