The Chainsword is aquired on Chapter 2, after it starts. You must complete an entire chapter firing only the Bolt Pistol and swinging the Chainsword. It's also worth noting that the Plasma Pistol you gain in Chapter 6 is a permenant swap; therefore you must complete this achievement before Chapter 6 to get this achievement.
USING GRENADES WILL VOID THIS ACHIEVEMENT.
Any easy way to get this achievement is to simply load the final checkpoint on Chapter 2 and finish the level with your bolt pistol and chainsword.