It takes a while to get the "Zombie Genocidist" achievement(53595 common infected killed). I have found a few ways to help speed the process along. First off, always play single player so you can betray your teammates and kill them without them booting you, or just play with 3 other friends who won't do any killing.
Here are some campaign tips:
1. Always let boomers boom on you. They are horde attracters. When you get boomed on, make sure the boomer leaves so it can recharge so it can boom again. If it starts attacking you, push it away. If it keeps attacking you, just kill it until you find another boomer.
2. Ramdom hordes happen on every part of every campaign, it just takes a while for random hordes to attack, so don't always rush into the next safe house.
3. Always alert hordes that are optional. Optional hordes are hordes set off by car alarms and other noisy things.
4. On the finale of every campaign, there will be 2 hordes and 2 tanks until rescue arrives, then there will be unlimited hordes and tanks. Take some time getting into the rescue veichle and kill some extra zombies before real danger comes close, such as tanks or other special infected.
5a. Special infected do not count toward your kill count, so don't waste time on killing special infected, but you should kill them before they kill you.
5b. Witches do not count toward your kill count either. Try not to even go near them. If they are in your way, try to make a teammate disturb it, unless you've already killed all your teammates. Never go for witch kills unless you are pro at CrOwning them (1 shot kill).
My way: This is the way I easily got the "Zombie Genocidist" achievement:
I play the No Mercy campaign normal mode, single player offline. I get to the beginning of level 5(the finale) and then kill all my teammates. I then open the safe room door, leave, go back in, and close the door. The door is unbreakable (except by tanks)and it is see-through. Boomers can boom through it, and as far as i know, smokers can't smoke you through it, but be cautious anyway. Once a boomer booms you through the safe room door, a lot of common infected come rushing to the door, unable to get in. Try not to kill the boomer. If you do, just wait for another one to show up. You have unlimited ammo, ultimate protecion, and infinite hordes coming running at the unbreakable see-through door. The only bad thing is that it takes a while and can get boring after a while, but it works. I hope I helped, and I'm sorry it's long, but that's the only way I can easily explain most cheats.