Mewtwo

In cinabar cave you have to go through the entire cave. This will include going up and down ladders and moving some rocks. Mewtwo should be at the far end of the cave as possible.

You go to cinnabar cave which is available for access after you help out the guy in island 1 by giving him a Ruby and a saphire. Then when you go to the cave make sure you have Pokemon that know rocksmash and Surf and if possible a masterball otherwise it will be very difficult. If you still haven't helped out the guy in island one here is how you get the ruby after talking to him surf north east and head north to get to the mountain at the beginning of the mountain you will see two Team Rocket guys blocking the way to an entrance beat both of them and make your way through the cave you will find the ruby. Then go to the lab to give him the ruby. Then he will give you a rainbow pass to go to islands 4,5,6,and 7. Head to island 6 and make your way to the dotted whole and in front of the door use Cut and it should open the door drop down through the hole and you will land at a place that has 4 holes one on each side of the cave drop down through the one on the northern end of the cave then the one on the west then the one east and finally the one on the south and you should be at the saphire take it then a scientist will steal it from you and tell you the other part of the code you heard from the team rocket guys at the mountain on island 1. Then from there go to island 5 and find team rockets base and once inside make your way to the room where the scientist is and beat the leader. Then the scientist will challenge you once you defeat him he will return the saffire and now return the saphire to island one and give it to the guy. Now you can go to cinnabar cave.

After completing everything go to Cerulean Cave.

He's In Cerulen Cave.