Easiest way is to load up the first level in a private normal multiplayer. Kill an enemy with a grenade, your main gun, your secondary gun, and a melee within a minute.
Really, any 4 different weapons (including melee and grenades) will work (not sure if different fire modes will count). So you could even get kills with the two starting weapons, pick one up, kill with it, and do that again with a fourth.
Edit: Heard from multiple sources now that yeah, it has to be in multiplayer. So don't bother trying it in single player.