To clone Mewtwo, you'll need to set up three machines:

You can craft these yourself (see next steps) or steal all three from the Radio Tower.

Put a Cloning Catalyst and Mew DNA inside the machine. Right-click on any of the three machines and the items will be placed into the Fossil Analyser.

You can obtain the Cloning Catalyst and Mew DNA from the Team Rocket Tower.

Fill the Restoration Tank with organic material. It takes 32 Bread to completely fill the tank.

Many food items work here - try different things out!

Watch as Mewtwo is cloned through four stages. The process runs automatically once all materials are inserted.

The Data Monitor will turn green when the cloning process is complete and Mewtwo is ready.

Use any Pokeball you want - right-click on the Data Monitor while holding it. Mewtwo will be added as Level 1 to your team or PC.

Here's a look at Mewtwo's in-game model.

Use the Rocket Armor item (infinite uses) to toggle Mewtwo between its normal and armored state.

The Rocket Armor can be obtained from the Team Rocket Tower.

For a Shiny Mewtwo (and thus a shiny Armored variant), use the Radiant Cloning Catalyst instead of the regular Cloning Catalyst.

Atena drops the Radiant Cloning Catalyst instead of the normal one in the special Team Rocket Tower