Details: After defeating Anabel, she and Looker will send you to Ms. Wicke on Aether Paradise, who is cooperating with The International Police after all the trouble The Aether Foundation caused. Go to Wicke, and she will initially not tell you anything about the Ultra Beasts, but rather the true reason why Lillie chose to go to the Kanto Region with her mother.
Wicke goes on to say the Lillie picked Kanto specifically because she read a book once that described how a trainer was once turned into a Pokemon like her mother, but was able to be turned back to normal by using his cell separation machine. The trainer is none of than Bill, and she went with her mother to Kanto to seek his help in possibly Healing her.
After this, Wicke will turn and walk away in the Labs Area of the Aether Paradise. Follow her, and she will eventually give you a number of Beast Balls. These special Poke Balls work well on Ultra Beasts - having a x5 Catch Rate to be exact - but aren't good on any other species. After receiving them, you must return to Anabel and Looker in the hotel on Route 8.
Talk to Anabel, and Looker will quickly burst into the room, saying there has been sightings of UB-01 Symbiont in both Diglett Tunnel and Wela Volcano Park. They ask you then to go to one of these areas and find it.
Nihilego can be found randomly in the wild Grasses and cave, like all the Ultra Beasts, and the music will change when you are nearing in on it. (You only need to catch on of its species.) UB-01, whose real species is known as Nihilego, will be at Level 55, knowing the Moves Power Gem, Mirror Coat, Acid Spray, and Venom Drench. It's a Rock / Poison Type Pokemon.
Like all the Ultra Beasts in this storyline, Nihilego will have one of its Stats doubled immediately as the Battle begins. It, specifically, will have its Special Defense increased. It also has the ability of Beast Boost, which will further boost its best Stat each and every Time it knocks out one of your Pokemon.
Catch Nihilego, and your first mission is now complete. Head back to Looker and Anabel to inform them of this, and to receive your next mission.