Instructions
Stock up on Ultra Balls if you decide to save your Master Ball or if you have already used it.
Go to Cerulean, walk past the Nugget Bridge and surf down toward the left side of the screen to find the entrance to the Unknown Dungeon.
Once inside, surf all the way to the right and head to the bottom platform to enter the maze.
Navigate the maze. The order is down, right, up, right, up, left, down, right and up. If you have navigated it correctly, you will find a ladder.
Use the ladder, and then navigate the second floor of the maze. The order is left, down, right and down.
Take the right path at the fork to find the second ladder.
Go down to a third ladder, located directly below the second. This will put you on the direct path to Mewtwo.
Save your game once you have found Mewtwo.
Battle with Mewtwo using your best Pokemon team. You can use your Master Ball to catch it quickly. Otherwise, you will need to work Mewtwo's hit points down as low as possible before throwing Ultra Balls at it. If you opt to use Ultra Balls to catch Mewtwo, it will take time and patience.