Back in Gen I, I played Colosseum a lot, and although we had no idea about tiers or strategy or anything, we quickly realised that Mewtwo was every team's ringer (although we never banned it - asking for no Mewtwo was like admitting defeat). There had to be a way to beat it, but the damage chart in Gen I meant that nothing could get an SE hit on it that wasn't weak back. Every single bug with Bug STAB was also part Poison (not even Butterfree couldn't beat it). When Gen II came around, Heracross had the same problem, and most of the Dark-types actually kind of sucked.
Bear in mind that I had no idea about the damage formula, STAB, or that a strong neutral attack could be better than a weaker SE one. Seeing the words, 'It's super effective!' meant you won.
I came up with two ingenious strategies to beat down Mewtwo in Colosseum I/II:
Focus Band Heracross. A 10% chance to survive getting OHKO'd by Psychic, but when it worked it was sweet. One time it hung on with the Band and Megahorn missed, but then the Focus Band saved it a second time the next turn, and it successfully KO'd Mewtwo back with Megahorn. I regarded this as vindication for my excellent strategy and declared supreme victory.
Pin Missile Jolteon. Oh yes. This was the only thing that got a Bug move that wasn't weak to Psychic in Gen I. Mine outsped Mewtwo as well, so it got those crucial 2-5 14BP hits in first. Thunder would have been far better, but it wouldn't have been SE, would it? Obviously I didn't use Thunderbolt, because I think you'll find it's weaker, therefore worse.
Of course, Gen II introduced the Dark type in order to balance Psychics, so the thing to use was the most powerful Dark-type...
Sandstorm/Pursuit Tyranitar. An incredibly smart set: Sandstorm/Pursuit/RS/EQ. Set up Sandstorm, then as the opponent flees in terror from 6% damage each turn, Pursuit ftw. The problem was that it was totally transparent, so I'd end up using 40BP Pursuit on a stationary opponent more often than not. Went back to Crunch, in an eye-opening 'some things are better than others' moment.
So my opponent switched things up in order to counter TTar...
DynamicPunch Mewtwo. The metagame today is a lot about managing risk to produce favourable outcomes. The game we played back in the day was more like Russian roulette. DynamicPunch was the only Fighting move that Mewtwo got (it was a Gen I TM iirc), so that was its best bet against TTar. The fact it only worked 50% of the time made it all the funnier.
Why not switch? Not for fear of Pursuit, because we rarely switched at all. Switching was like a little admission of defeat, like your current poke couldn't get the job done. It was far more fitting (and insulting) to simply KO your opponent's counter and keep going. Also, if your opponent had Mewtwo out, the thing you switched in was going to die too, so what's the use? Teambuilding wasn't really something we considered either, and there weren't a lot of great Fighting types in Gen I/II anyway.
Plus I had my own Mewtwo...
Swift/Barrier/Psychic/Recover Mewtwo. Because that's what it came with. I also subscribed to the idea that pokes should have weaker moves to deliver a coup de grace, and Swift was pretty. Moves that weren't Psychic were basically there to fill out the set anyway.
After finding the Missingno glitch, which let me spam TMs on everything I could, I went with Blizzard/Thunder/Hyper Beam/Psychic, because fuck you.