You are given the flame blade at the start of the Highlands level. You can toggle back to the basic sword with the right stick.
The game has a hub area that allows you to replay levels.
NOTE: This hub is only accessible until you enter the Old City level.
I went back and got this achievement after having played through the Highlands level once where I had used the flame blade. I imagine that it might be easier once you get the frost axe, but I was impatient so I did it with the basic sword.
You need to play through the first two areas of the Highlands level and once you reach the tower (after the Banshee scene), the achievement unlocks. I took the backdoor shortcut through the cave so that's acceptable.