I tried to do it the intended way, but found it too difficult. I was able to cheese it by staying in the starting area and killing the enemies that spawned to the right.
The pistol is crazy accurate in these games so you can pick enemies of from afar with a few shots each, and in this case they are firing shotguns which are very ineffective at long range (the game stimulates them as having unrealistically wide pellet spread, so even if a far-off enemy gets a pin-point shot you will only take minimal damage).
I remember playing over the collage NetWare LAN and winning people who had better but less accurate weapons (usually the shotgun, or the double in later versions, as we found that the most cathartic) simply by keeping my distance. Works until someone gets close from behind, at which point if you respawn somewhere convenient you can find the bugger PDQ, and pick him off with the pistol for revenge. Even works against the rocket launcher, just make sure you don't get hit directly (d'oh) or hang around where it is easy for splash damage from misses to ruin your plans.
It is a valid method for many DOOM-style games (as they were called in my day) and their offspring. Works well in HL2 where you can spam the trigger button as fast as you like and the basic pistol will fire at that rate without a limit (other weapons have a minimum shot latency).