Here is a simple step by step guide on how to catch the Mewtwo I caught. You must have Pokemon Black and have beaten the first gym.
Note: This is probably a glitch so you might not get the same result.
- Enter Wellspring Cave (Cave on Route 3). Make sure to save.
- Walk alongside the right-hand wall until it bends.
- Run into the wall on the spot right after the wall bends.
- Run in to the wall 6 more times.
- The wall should collapse and you should hear a glitched Mewtwo say "Mrooowow! Mroo!" If not, turn the power off and try again.
- Walk past the crumbled wall into a hidden area that is actually a cave in Pokemon Red (I found this out later).
- If you are lucky, there will be no more glitches (If so, turn off the power and try again). Approach the Mewtwo and it will challenge you.
- Throw a Quick Ball at it or decrease its HP and catch it with a Dusk Ball.
- If you catch it, save immediately(If you don't save, the Mewtwo will disappear after you leave the hidden area. I experimented with this).
- Congratulations! You just caught a glitched, impossibly strong, and awesome Mewtwo!