This is a multiplayer achievement and can only be done in ranked matches.
In Golden Gun mode, there is a Golden gun that everyone is trying to get. If someone has the gun and then dies, the gun stays on the floor until someone else picks it up. When someone has the gun, they will be shown on your map as a gold marker and on your screen as a gold gun when you are looking in their direction. Be careful when you get close to them to melee them because they will kill you in one shot. Try to get them from behind or when the gun is on the ground and everyone is trying to get it, wait until someone has it and then melee them. To melee someone, you have to click the RS.
If you need help with this achievement, please use the Quantum of Solace Achievement Trading Thread.