This is easily done on easy. Doing it on the harder difficulties may not work so well as melee combat is a bit of a risk. To get this you need to kill an enemy with a gun, then get a melee kill then another gun kill etc. You need 5 kills with a gun and 5 with your fists by switching back and forth.
Defeat 10 enemies in a row, alternating gunplay and hand-to-hand