This is an easy to get and easy to miss achievement in the early chapters of this game.
The wording is a little off but it means a 10 zombie multi kill not 10 Multi Zombie kills.
So the set up is simple have a grenade and go to right before the final checkpoint in the chapter The Outskirts. there is a lever that you have to kick to set off some explosives to then drop down onto a raised platform.
While on the platform try to kill the Barrel zombies by crouching and shooting at the left one and standing all the way to the right on the platform and holding
for a further grenade throw. The barrel zombies don't effect the pile up of the normal zombies, they just ruin your throw by staggering you giving the normal zombies a chance to spread out.
After you have killed both of the barrels wait about a minute to a minute and a half and you should have anywhere from 10 to 14 zombies piled up in the right corner.
Make extra sure to recount as same outfit zombies can stack, and make it hard to tell if it is 3 sailors and a cop or 1 sailor and a cop.
After you have counted out 10 or more in the right corner jump off the left side and throw a grenade into the crowd
and wait for your achievement to pop.
If it didn't pop like it didn't for me on my first try simply die and retry!
TL:DR Watch this and skip that wall of text