The second EX side mission for Pokémon Legends: Z-A involves heading back to Lysandre Cafe, and the Team Flare base hidden beneath, in search of a very powerful legendary Pokémon. Since this is considered endgame content, you should complete the main story of Pokémon Legends: Z-A before trying to tackle Side Mission EX2: Project M.
To start, open up the main menu of your game and go down to Link Play. You access this through the Mystery Gift just like the Diancie EX1 Side Mission. Thankfully, while this does require internet, you don’t need an active Nintendo Switch Online subscription.
Mewtwonite X and 
Mewtwonite Y Mega Stones and the opportunity to catch 
Mewtwoin Side Mission EX2.
Once you have your Mystery Gift Mega Stones, fast travel to the Lysandre Cafe. Go inside the cafe and then through the big red door in the back. Head down the small stairs and go straight ahead to the red elevator doors. When you interact with the elevator, choose to go to the bottom floor of B3F, which you didn’t use in the main story.
Go a little down this dark hallway and look for a small set of stairs to your right. Head up these stairs and enter the dark room beyond.
There is a blue screen with some schematics in this ominous room. The systems in this room reacts to your Mewtwonite X and Mewtwonite Y Mega Stones, restoring power to this area. You're then asked if you want to release the locks. Choose this option to free Mewtwo.
At this point Mable contacts you commanding you to Mewtwo heralding the official start of Project M. Remember to track the quest by pressing +.
Mewtwo awaits you at the end of the room. This gives you a moment to pick the right team and ensure you have enough Poké (or specialty) Balls to ensure you catch it. It is also recommended you save your game.
Whenever you’re ready, approach Mewtwo to begin a battle. This is a powerful legendary Pokémon, so be sure to bring along a high-level team or have yourself a 
Master Ball ready to go.
(Optional) Facing off against Mewtwo a level 70 Legendary 
Psychic Pokémon. That said, 
Dark Pokémon are completely immune to Psychic moves, thus Pokémon like 
Absol or 
Greninja are solid picks. However, your goal is to catch Mewtwo to complete the mission, not just beat it. If you have a Master Ball or some luck on your side, you can end this fight before it even begins.
Be careful not to let Mewtwo faint because if you miss the single capture chance at this point, the battle resets and you have to go again. Be sure to check out our guide on Specialty Poke Balls and Capture Rates for more tips on how to deal with this.
After finally capturing Mewtwo, Mable appears to give you a quick breakdown of why Team Flare had Mewtwo in the first place. Finishing this conversation completes the Project M EX2 Side Mission.
Giving your Mewtwo either the Mewtwonite allows it to Mega Evolve into 
Mega Mewtwo X or 
Mega Mewtwo Y. Mega Mewtwo X is a Psychic/
Fighting type with unbelievably high Attack and Speed. Mega Mewtwo Y on other hand, is a pure Psychic-type also with great Speed and incredibly high Special Attack. Want to learn more about these special Side Missions? Be sure to check out our EX Side Mission guide or track your progress on all of the game’s Side Missions without Side Mission Checklist!
