It is catchable. But the way I caught it was different than all of yours... You might want to have some strong pokemon. Its pretty tough. You have to be able to go to the seven islands. Beat the Elite 4 20 times. Go to Mewtwo's cave. Run around the spot mewtwo was in. Fight 10 of the pokemon that appear and defeat all of them. But it has to be in that spot. Then fly to pallet town. Prof. Oak will be outside walking around near your house. Talk to him. He'll tell you that Hes very proud of how far you've gotten in pokemon or something like that. Then heres the part where you NEED your BEST pokemon. You have to fight him. He has 1 Johto pokemon. His Team is : Charizard Blastoise Venusaur Arcanine Dragonite Tyranitar (where do you think your rival got his from :D) After you beat him (if you can), he will give you a paper. You have to take that paper to island 7. Walk around alittle whil then go back to the dock. There will be a different Capt. There. He will tell you that the other capt. Suddenly got sick. Then he will see that paper you have. He will ask for it. Than he will take you to a little island in the middle of the sea. You can find Incredibly strong pokemon on this island ( Dragonairs, Steelixs, Arcanines, etc.) . You will find a cave. If you go in, there will be a lot of statues. Press A on the Gold one in the center. It will start glowing. After a few seconds it will break. Then all the others break. Finally, Mew will Fly out of nowhere and you fight him.
Hope I helped :D! Also in Fire Red, If you do this cheat you will fight Celebi instead of Mew.
Hope I helped :D! Also in Fire Red, If you do this cheat you will fight Celebi instead of Mew.