Instructions
Enter the cave. Go to Cerulean City and walk over the bridge to the north. There's a body of water on your left. Use a water Pokemon to surf over the water to the cave entrance. On previous trips, a guard would have kept you out, but after defeating the Elite Four the first time, he is no longer there.
Find the ladder. From the entrance, go to your left, then surf over the water until you can go no farther. The ladder will be in plain sight there. Go up it.
Get to the second ladder. After climbing the first ladder, walk down a screen, then to the left. At the next intersection, go right, then up, then right again. This will bring you to two paths going up. Take the right-hand path. At the end of that path will be the ladder, which you will need to descend.
Locate the third ladder. From the bottom of the second ladder, follow the path to the left until it ends. Follow the downward path, then take the stairs at the end of it. The ladder is at the top of the stairs.
Walk to the next ladder. From the third ladder, take the path that goes upward until it ends, then take the path on the right-hand side. Walk to the bottom of the screen, then go to your right. The ladder will be in the right-hand corner of this room. Go down it.
Climb yet another ladder. The previous ladder puts you at the head of a set of stairs. Go down them. Take the right-hand path until you find a ladder for you to climb.
Go down two more ladders. The last ladder will put you on a path that only goes one way. Follow it, then go down the ladder at the end. This ladder will put you on another one-way path with another ladder at the end.
At the bottom of the final ladder, there's a body of water. Use your water Pokemon to surf to the right, then up a screen.
Exit the waterway, then find the second lake.
Surf downwards and to the right until you find a small island. At this point, you should save your game. Immediately.
Climb the stairs on the small island to be attacked by Mewtwo.
Battle Mewtwo. He is level 70. Any Pokemon below that will be useless. Considering his sheer power, you will want Pokemon who are at least five levels above that. Mewtwo uses Psychic attacks, Swift, Barrier, and a healing spell called Recover. Abilities that stop a Pokemon for a few rounds, such as Sleep, Paralyze, and Freeze, are almost required to give you time to heal and launch attacks. As with any capture battle, weaken Mewtwo enough to capture him with a ball. If you have a Master Ball, using it at the start of the battle is advisable.