As Champion, you can now access Cerulean Cave, which was previously off-limits because of the powerful Pokémon inside. This is where Mewtwo fled after destroying the research facility on Cinnabar Island.
This is a treacherous, sprawling cave, so make sure that you are well-prepared. Stock up on Ultra Balls and bring the Super Rod along, too. Bring a Pokémon that can use Surf, and pack that Master Ball if you still have it. Mewtwo is one tough fighter, even harder to catch than the legendary birds, so you're in for a long battle if you've used it already. Head north to Route 24 and surf south along the river to reach the cave.
Walk up onto the rock platform and climb the ladder to the second floor.
Loop around to the east, grab the PP Up, and take the ladder in the northeast back to the first floor.
Go down the stairway and surf to the west. Grab the nearby Max Elixer, and climb onto the rock platform just west of that. Pick up the Nugget and climb up the ladder.
Head east through the maze to find a Full Restore, then continue on to find the next ladder.
Go west and surf across the water for another Full Restore, then climb back onto the rock platform. Follow the southern trail to the next ladder.
Pick up the Ultra Ball, then follow the trail to the ladder in the northwest.
Take the next ladder down to the basement floor.
Head northeast from the ladder, and grab the Max Revive from the north-central rock platform. Follow the trail to the southwest, and climb up onto the central rock platform to collect another Ultra Ball. Surf across the water and cut across the rock platform in the northeast. Surf south to find Mewtwo alone on its island.
Not only is it the strongest Pokémon in the game, but it's already at level 70! Be sure to save the game before approaching it, as you have only one chance to catch it. Mewtwo can restore its health nearly a dozen times with Recover, and is only vulnerable to Bug-type attacks. However, the threedamage-inflictingBug-type moves are fairly weak. It may be better to use the legendary birds, as they are nearly Mewtwo's equals in terms of power. freezing it with Blizzard, Ice Beam, or Ice Punch is the best way to catch it, as it cannot attack or recover.
With Cerulean Cave cleared, the storyline is now complete. Even though there are no more Gym Leaders to defeat, you still have a task to finish: completing the Pokédex for Professor Oak. If you manage to do it, you can show it to the Game Freak employees in Celadon for your reward.