There is an easy way of doing it. Start Miamy level (the one on the beach) with Kate. Go to the phone booth and make a call. This will spawn a couple of zombies which will try to infect everyone.
Zombies make it much easier for 2 reasons:
1) killing a zombie doesn't alert anyone
2) zombies never leave corpses
Also they are kicked right away, you don't have to kick them unconcious.
So just kill zombies as they infect everyone, and the acheivement is yours.