I was having a lot of trouble taking it down with random people online, but here's what worked for me in the end. I've been able to beat Mewtwo 3 times with random people with this build.

Mew @ Metronome
Ability: Synchronize
Tera Type: Bug
EVs: 4 HP / 252 Atk / 252 Def
Adamant Nature

• Leech Life
• Swords Dance
• Misty Terrain
• Mud-Slap

You'll still need a few Mews with Struggle Bug or Snarl to cover that gap. In general, I found that mud slap was proving to be more useful in keeping me alive than Light Screen because of the impacts to Mewtwo's accuracy while also charging the Tera orb.

3 mud slaps up front keeping and eye on your teammates health. If anyone is near half, heal cheer. Then 2-3 Swords Dance, terastalize, then start spamming Leech Life.

Mud slap and Swords Dance in response to Mewtwo nullifying effects.

The biggest challenge was keeping my teammates alive more than myself. Leech Life with 2-3 Swords dances will keep you alive easily. Make sure you keep an eye on your teammates health and heal cheer as needed, especially if no one is using life dew.

Edit: Forgot to mention why Misty Terrain is there. You'll need to use Misty Terrain right before you break his shield because he's going to use Rest right after the shield break and having Misty or Electrifying Terrain in place will prevent it from healing. In general, had a few cases where my teammates didn't appear to know that, but most people knew about the need for struggle bug, so I dropped struggle bug for Terrain