The Plasma Pistol is obtained in the manufatorum, during Chapter 6. The Plasma Gun can be found during chapter 12. This achievement can be gained as easily on Chapter 7, provided you do not use any weapons other than the pistol. Chapter 10 is a good Chapter to attempt this as well, as your primary enemies are turrets. There are, at most, 15 to 20 Orks on the mission, and plenty of cover when dealing with the turrets.
Note: Using melee, executions, or grenades will void this achievement.
You can get this achievement fairly easily by loading the final checkpoint of Chapter 6 and finishing the mission with just your Plasma Pistol. Deal with any Nobz you find by overcharging the Pistol when you see them. Remember to complete the objectives as fast as possible or else you will be dealiing with unlimited enemies.