This must be done in coop mode (you can be in a game by yourself, however). There are several methods to killing people, despite a loadout of only two weapons by default:
Takedown (RS near basic enemy type)
Also, it's possible to pick up another weapon, kill someone with it, rinse, repeat. Four in a minute should be possible at many parts of the game in single player and coop. Load up Western Europe. Kill an enemy with your main weapon, pistol sidearm, and melee. Then grenade the last. It'll pop after the 4th kill.