When you kill an enemy, you will see some skulls in the top right corner and one of them will have a cross through it. That is your combo counter. You'll see all five lit up at first and one by one they will dim until it reaches the first skull and that is the end of your combo. You can reset the timer by hurting an enemy or taking damage, or obviously killing an enemy. When you kill the next enemy, the next skull will have a cross through it.
Cross out five skulls to get this achievement by killing five enemies.