Edit: Per Fiezza below, powers may not contribute to getting kills, so it is wise to do gun only runs to make sure every kill you get is counting.
Edit 2: I forgot to mention that I was using the M-490 Blackstorm Singularity Projector for my first few runs and I was only seeing an increase of 3 kills per run even though it was wiping out every enemy. Best of stay away from that gun specifically as well and maybe all heavy weapons.
This method will generate between 40-60 kills per run depending on your luck/weapon levels. Each run takes anywhere from 2-4 min. I was able to grind out the last 1000 kills I needed in about 1 hr using this method. I was on the casual difficulty to make enemies as easy as possible. This method uses ME2 since that is currently the only reliable game that tracks, even with the update.
The mission you are looking to use is "N7-Abandoned Mine" which is found on the planet Aequitas (Minos Wasteland, Fortis). Credit to Neo Yggdrasill for his comment in the forums pointing me in this direction.
I recommend a save before you go to the mission in your cabin on the Normandy for an easy load to check your progress.
After that is done, land on the planet and make another save incase you mess up and end the mission. Now progress through the mission until you come to a path that branches off in 2 directions. Make a separate save here.
From this point, move up to the right and onto the overhang, notice the crate on the right that has an ammo resupply, do not pick this up yet. Once you enter the overhang, enemies will spawn. Go to the top of the ramp but do not go down to the bottom. simply let the husks run to this ramp and up at you. Aim for their torso for an easy 1 burst kill with the assault rifle. Use the ammo on the crate as required to finish out the wave. You will get an auto save once all enemies are defeated.
Once complete, head down and collect ammo as needed, there is always one right at the bottom of the ramp. Then head in the doorway to the right and continue into the room ahead. Once you have cleared the doorway, quickly pop back out and look to your left. There will be waves of 3 husks that spawn for a total of 6-7 times. Simply keep killing these until they no longer spawn. you will notice another auto save happening at the bottom.
Reload your save from the bottom of the ramp earlier and repeat as needed.