You can get this achievement easily by just doing the tutorial in which you will be tasked to convert civilians into zombies

This achievement can be done in 3rd mission in prologue where you rescue Dr.jazz.In this mission 1st use zombies to convert the civilians near the tents don't convert all leave the ones that runaway don't chase and then just proceed to liberate Dr.jazz by killing the guards once you release jazz.A group of guards will come from west just divert them with zombies and use jazz[whom you can control once released] to kill a civilian.This triggers the achievement

Next mission[worrisome news]where you will be tasked destroy a radio tower by usind dr.jazz.In this mission you will be given zombie bomb.now select some normal zombies and attack the entrance when they start attacking some guards will come together to shoot them now use one zombie bomb to attack which will kill more than 5 guards thus triggering the achievement.

This mission is tied up with level worrisome news.kill all the guards and use dr.jazz to disable the tower and completing the mission.This triggers the achievement

In the Mission Dr.Stefano vs Neilman.you need to release the prisoner and kill neilman.Beware when you storm the building,neilman started to attack the prisoners so be quick and kill him before he kills all the prisoner.if he kills all then the mission is failure.once you killed the neilman the achievement is triggered.

There are 14 missions in single player.once the 14th mission [survive] is completed the achievement is unlocked.In this mission you have to survive close to 6 waves.In the final wave you have to kill a guy called evilcash and once you have killed him and all the guards the mission is completed

Tip: Tutorial is the best level to do this. It's simple by the way.
1. After start the level, convert all the citizens to zombies. Stop your units a little bit far from the police creating a small group of zombies.
2. Use ONE fast moving zombie(green coloured shirt) to move until one police start to follow him.
3. Move back your zombie making the police walk to inside/beside your zombie group.
4. Select your zombies and press H (hold) repeatedly to avoid zombies attack.
5. Finally when the police is among /very nearby the zombies, stop pressing H button and your zombies will kill him
6. Repeat this process until to kill all enemies.
7.After each killing Check zombies life and remove the most damaged zombie somewhere to avoid casualty
8. Achievement Unlocked

You can kill one or two cops per time.

It's simple, not easy :)

Thanks to Jasiel Macedo for the tip which was based on level 1 but I found tutorial to be far easier