This is a multiplayer achievement and can only be done in ranked matches.
This is easiest done in Golden Gun mode. To be the top player, you must have the top score. If you win a match of Golden Gun then you have the top score. To get a lot of score in this game mode, you can kill people with the Golden Gun, pick up the Golden Gun, or kill people who have the Golden Gun. You only get 1 point for killing people when neither you nor the person you kill has the Golden Gun but your score will add up if you get a lot of kills.
If you need help with this achievement, please use the Quantum of Solace Achievement Trading Thread.