Oh, yeah >.>
Then other than fire-types would collapse in that battle. There would be no one left alive. If you take more than 20 Beedrills and put them up against any of your Pokemon, your Pokemon will collapse faster than the Beedrills. It's cruel, but IMHO it seems quantity > quality. (Unless we're talking about Ash's Pikachu :\ )
Psywave has the benefit of area damage and it will certainly push the Beedrills backwards. It's a lot better than sending single Psybeams to take them down.
Psywave is a wide-spread attack, if ordered, so dodging that could be fairly hard. (But possible, nevertheless.) Psychic, as unbalanced as it seems, is quite undodgeable with physical speed.
And there's always Hidden Power [FILLER] which lets them take down anything they want. Hidden Power Bug occuring in 20+ Beedrill is possible, but not all of them will carry it. (Let alone, be smart enough to use it).
I know, but saying that Alakazam wouldn't be able to handle a swarm of Beedrills is kind of unfair. Seeing as Alakazam has much greater chances to do that than many of the grass-types for example.
Psychic can't do everything, saying/using that excuse in a fic is lame, I know. Psychic is telekinetic attack, or it can be used in a form of psychic blast. Psychic can do a lot of things, but not anything. The best option is teleporting out, not very exciting, but wise nevertheless. Then they could return back to the scene later on.