You will start coming across EMP Grenades a short while after finding the shotgun.
For the achievement you need to kill 20 enemies with these grenades.
(You can hold a capacity of 8 grenades in your inventory, and ammo dumps are aplenty.)
to quickly throw the grenade, or hold down the
to bring up an adjustable arch to help you aim where you need your grenade to land.
Depending on the difficulty setting it takes 1-2 EMP Grenades to kill a soldier.
(The achievement will go by much faster if you throw your grenades into grouped enemies. getting more kill per grenade.)
The achievement and kills are accumulative, so your grenade kills will not be reset, or lost if you die during a mission.