You will probably unlock this achievement naturally as you play. This solution is just to clarify what it involves. Whilst rare at the start, the later stages feature several rooms where you will be swamped by drones and surrounded by EMP's.
Drones are the orange blobs that float towards you and do damage. EMP's are the fixed towers that explode across a circular area when they are hit by a ball.
You can see an example in the video here
. (Not my video, credit and thanks to horheristo)
The achievement unlocks once 100 drones have been destroyed by an EMP blast.