A successful first run of the legendary Pokemon happened earlier today. In the coming weeks you too will have a chance to capture Mewtwo.
Use your Master Balls!
Only way to capture this Legendary Pokemon is to participate in exclusive raid battles. According to the website, this is what they had to say about this feature
Exclusive Raid Battles are similar to existing Raid Battles, with a few notable differences. Exclusive raids will periodically appear at Gyms around the world; however, unlike existing raids, Trainers will be invited to join an Exclusive Raid Battle. To receive an invitation to participate in an Exclusive Raid Battle, Trainers must have successfully completed a raid recently, by defeating the Raid Boss, at the Gym where the Exclusive Raid Battle will be taking place. The invitations will include advance warning of when the Exclusive Raid will take place, giving them ample time to coordinate with other Trainers before taking on the powerful Raid Boss.
Neat. In addition to this, Articuno, Zapdos, Moltres, and Lugia, all four of these Legendary Pokémon can be battled in Raid Battles from August 14 through August 31.