BioShock Infinite

I ground out my 20 kills at the checkpoint after leaving the Hall of Heroes shortly after grabbing Shock Jockey. The chapter you want to reload is "Return to Hall of Heroes". (thanks perfectdozen for clarification) You can tear in a Mosquito, which is a floating automated machine gun, right in front of you in the air in the back of the area. This Mosquito isn't very tough, but it has a good line of sight to the enemies below. Between Slate's men and Comstock's men fighting, and them shooting at you, it should claim a few kills with each of its lives. I had two enemies with shotguns rush me on the balcony while I hid back and let the turret do its work.

You can help it along by putting a few shots into each men to wound them to make it easier for the turret to kill. If it gets destroyed, you can re-tear it back into existence a few seconds later while you hide on the balcony. Once you let it kill everyone in the area, restart checkpoint and you return immediately where you were outside the door for more boosting.

There are two allies before this one in the game, but the checkpoints are further away, or it will only help kill one enemy. This location only took me a few minutes.

*************Spoiler Alert*************

After you acquire Elizabeth's Tear ability, which is obtained automatically as part of the story, you can use it to summon in allies who will automatically attack enemies for you. These include Motorized Patriots (the robot George Washington guys), Mosquitos (flying turrets) and stationary Automatons which either shoot rockets or fire a machine gun. You must get 20 kills using any of these allies. You can weaken the enemies a little with your guns and vigors, but the ally you summoned must get the kill.

As with most of the combat achievements, it's recommended to do this on Easy difficulty. I played on Hard and only managed 10 kills towards this achievement by the end of the game.

Hey guys,

I made a video on how to get this achievement.

Basically you want to go to the Return to Hall of Heroes Plaza chapter.
Once done run down to the sky rail at the end and bring in the mosquito to your right.
If it gets destroyed then you can simply open another tear and after a few seconds you can open the mosquito again.

Rinse and repeat!

Let me know if this helps!
I hope to get more videos soon.

SPOILER

S P O I L E R



Easiest place - last battle with Siren in front of the gate to the Comstock's house.
Get on the balcony above the sniper rifle tear and hide behind the left column.
There is a Mosquito Tear flying above the square. Keep calling it while Siren resurrects enemies:)))
Just watch out for the melee enemies - they sometimes run to your position.
Got it on 1999 difficulty.