World War Z

I was struggling a bit getting this achievement the normal way with guns and being cautious. The way I got it was using the Slasher class. You need it to be at least level 17. This way you can buy the perk:

Heavy Metal I. The character starts with an improved Forrest Warrior Chainsaw, dealing 50% more damage and having 50% more fuel. All Forest Warrior Chainsaw pickups are also improved.

Now equip it from the start and only use your chainsaw the whole level. You can chainsaw a lot of zombies and slash your way through groups without hitting your teammates, because this is disabled by default! The improved version of the chainsaw gives you a lot more fuel to maintain the weapon for a much longer time. At least untill you get a new one somewhere in the level.

Extra Tip: Use the LT over the RT attack, because this kills a zombie with the least ammout of fuel.

A lot of the achievements can be gotten very early on the first level - New York - Descent while playing on easy. You can combine this one with the most effective way achievement using only the pistol. Pick any class and only use your side arm to kill zombies not near any teammates (including bots). Then just melee the rest. Your AI teammates will do a bulk of the work. You can also use your starting equipment as well as deploy any defense, just don't use the stationary machine gun. Also do not use any heavy weapons (rocket launcher etc).

Once the level ends, you will get the achievement.