This must be done on Normal Difficulty or higher. You must simply select the Flamethrower as your primary weapon the entire time, starting from Level 1, and also beat the game. You do not have to use only the Flamethrower, you can use any other extra weapons and abilities as much as you want. You can also die and continue as much as you want. As long as you reload the same campaign, you can also stop playing and resume your progress at another time. Between each level you will return to HQ and see icons that show if you still meet the requirements for this achievement, and others, on the currently loaded campaign.