For this achievement you have to kill a Robot by shooting it's head, which should result in an explosion, killing at least 1 enemy which is close to the Robot.
Deadeye is the aiming mode in the game (
Button), and you must make sure you aim to the robots head in Deadeye mode.
I recommend starting a new world with your Agent (it will keep your orbs and unlocks), and try to go for the Roxy boss mission first by attacking at least 5 Monorail Stations. Also use the PDW as that's what worked for me.
After traversing a bit through the tower, you'll come across some batches of robots spawning in, try your luck against these enemies, and if nothing happens, then leave the tower and return after about 2-5 minutes. Repeat this until hopefully luck hits and achievement pops up.
This achievement can take either minutes or hours depending on your luck, as the robots heads don't explode all the time. It took me so long I was sure it was glitched, but no I just had the worst luck.
EDIT: According to some people, you will have better luck doing this achievement on a new world if you haven't got it yet on your first world. So if you aren't having any luck and you're far through, or even done with one world, then i'd recommend starting a new one.