Chapter 14: Ultra Space
Head north through the entrance and you'll arrive at the Altar of the Moone (Moon version) or Altar of the Sunne (Sun version). Head up the long set of stairs after a cutscene. head to the right and stand on the platform opposite of Lillie. A cutscene will play where Lunala (Moon version) or Solgaleo (Sun version) will appear and take you into Ultra Space.
Head to the north a bit and you'll quickly run into Guzma. After a cutscene, follow Lillie up ahead and watch another cutscene. You'll have to battle Lusamine again after she's been engulfed by an Ultra Beast. She has a Lv. 50 Clefable, a Lv. 50 Milotic, a Lv. 50 Mismagius, a Lv. 50 Lilligant, and a Lv. 50 Bewear. After you've defeated her, Lunala/Solgaleo will seperate Lusamine from the Ultra Beast. You'll then be taken out of Ultra Space.
You'll now have the opportunty to battle against and catch Lunala/Solgaleo. Make sure to save your game before you interact with Lunala/Solgaleo. You can use the Master Ball to make these easy if you wish, but we reccommend saving it. Lower it's HP as much as you can and throw Ultra Balls, it's not too hard to catch. Once you've caught your title legendary, another cutscene will play. Nanu will arrive afterwards and ask if you'd like to go to Tapu Village with him. Say yes.