There are 3 different allies you can bring through Tears that will help you get the kills needed.
Mosquito: Flying mini blimps with guns
Automated Turrets: Gun/Rocket turrets
Motorized Patriots: The robots who carry mini-guns
These will become more frequent after saving Elizabeth. Hold to create them and let them wreck havoc on your enemies. If you switch to a different tear, they will eventually be usable again. You can take cover and keep triggering them if you want to grind it out, or you can unlock the achievement as you play casually through the game.
It may help to shoot enemies lightly before you use a summon tear so that the allies have easy targets to kill. allies include Mosquitoes, patriots, and automatons.