Disclaimer: Kills carry over across all saves, and you don't have to save for them to count. This solution is for people who just want to grind the achievement as quickly as possible, even if untrained in Assault Rifles. You must have command of the Normandy before you can follow this solution.
Killing friendly critters counts towards your kills. Go to the planet Eletania (in the Hercules system of Attican Beta) where you will find several colonies of little monkey aliens. Simply drive up to one in the Mako, save your game, and shoot each of the monkeys with your assault rifle of choice. When they're all dead, reload your save and repeat.
There are about ten monkeys in each colony, so you'll need to do this fifteen times at most. Note that there are poisonous toxins in the atmosphere that will eventually kill you, but you should be able to get all the monkeys before then.