To earn the Kickoff trophy, you have to defeat any enemy using only kicks. If you haven't made much use of kicks, you need to hit dodge and immediately hit attack in very quick succession. You'll see Cal make a low kick when you get it right, otherwise you will likely slice your opponent in half with a lightsaber if you get it wrong.
The opponent cannot be hit by anything else, including friendly fire, for this to work. Personally I find it easiest to whack the difficulty down, find an isolated stormtrooper, and just stay close pressing dodge and attack rapidly to kick them to death. The trooper right at the back of Zeffo's abandoned village, before you hop over the ledge and up the hill, works well for this.