Mass Effect

This achievement can be obtained naturally by completing the main mission "Colony Gone" at an early stage in your career. After battling through tons of no-organic Geth the final two sections: Minimize Casualties & Destroy the Thorian will be chalk full of Thorian creepers and Asari clones, not to mention a dozen humans if you choose to kill them for the renegade pts.

You'll likely have to repeat some of the five waves of Creepers and Asari clones, but that will only help stack up the body count. All kills are accumulative even if you die.

One way to speed this achievement along is to go to Eletania in the Attican Beta cluster. There's a side quest there to find a missing data disk, and it has you checking several colonies of indigenous monkeys for the missing disk. All of these monkeys are killable and count as organic kills, for ~50 on the entire mission. They also count toward the weapon achievements (pistol, shotgun, etc) as well, serving as a good way to score numerous kills with unskilled weapons, since the monkeys don't fight back. You will get a few Renegade points on the first kill.

And if you want to, you can run over any animals with the Mako to get this achievement. Because I got this achievement by running over a deer looking animal on my first playthrough.

These kills do count towards this achievement.

I got this achievement while doing the survival in the DLC. The kills here count towards all kill achievements and as the enemies continue to respawn you don't have to work about running out of enemies to kill. If you die reload a challenge and keep going.