To gain this achievement, you must have 1000 kills in online matches. Player or ranked; both count.
The quickest way to earn this achievement is as an SCU agent in Bum Rush. You can get between 20-30 kills per round once you've gotten good at this, regardless of how many bums you have playing. If you want to boost the best way to do it would be to set up a 2 player game in Hangover and just take turns as SCU, running straight for the agent if you're Influenced.