The first mission has you investigate a deal going down between Team Olympus/Asgard and Team Rocket. The first battle is a double battle, so be prepared. Battle your way through generic grunts until you come across two main grunts from each team finalizing a deal. An officer will attempt to arrest them after some dialogue but they will flee. You're given a Max Revive for your work.
Mission 2 has you rescue Professor Oak from Team Rocket attempting to steal a device from him. You arrive in Pallet Town which is filled with Team Rocket grunts, so you will have to battle your way through. After reaching him in his lab, you must battle Oak!
You first must have the Necro Badge to attempt this mission. This time it's for real! Team Rocket has tracked down Mew to its natural habitat, Faraway Island. You must stop Team Rocket by battling the Grunts up to Giovanni himself! Defeat him to stop this madness!
The player must first obtain the Swarm Badge to obtain this mission. It seems Team Rocket left the island after their defeat with a tiny piece of Mew's DNA in their possession, required to clone this legendary and mythical Pokemon. This mission takes you to their base to stop Team Rocket from attempting to clone Mew!
The Team Rocket Base is filled with grunts, which you unsurprisingly have to fight. When you get to Giovanni, he uses a level 45 armored Mewtwo like the first movie. It is Psychic/Dark type and has the same stats as a normal Mewtwo, but it has the Hubris ability (think Moxie but for Sp. Atk).
You need to have earned the Kinectic Badge before you can attempt this mission.
You are invited by Mewtwo to an island where he captures the other trainers, and you have to destroy his clone machine. This is similar to the plot of the first Pokémon movie. Then you must proceed upward through a maze guarded by trainers named after the Seven Deadly Sins.
You can get through easiest by battling only four of the trainers, just go straight up. They're tough, about the same level as Miranda. If you've beaten her, you should have no trouble.