The first chance you will have to get this achievement is in Challenge Mode level 4 "Crossing Paths", unless you you play Arcade Mode first.
You can create trails of a certain colour by pressing the coloured buttons (
,
,
,
) on the Xbox controller, the colour of your trail will match the colour of the button you press.
= Green
= Red
= Blue
= Yellow
Now you know this, what you need to do now is to create a trail by pressing one of the coloured buttons to match a colour of an enemy, if an enemy matching the colour of your trail hits your trail it will kill the enemy.
Achievement unlocked, it's as easy as that!
I also made a gameplay video of the level if you would like a look: