To unlock this achievement you will need to have the perk "Bathe in Fire" active. To quickly get this achievement I would recommend you do not have the "Bullet Breath" or "The Flow" Perks active also.
First, play the game as normal and get some slammers, runners and bombers (Bombers can be recruited at "The Gnorp Propulsion Lab". You will want to trigger a compression event or have the "Zybellium Mastery" Perk unlocked. When you collect the Zybellium shard you will want to spend it on "The Slam Club" upgrade "Fire Breath" and have your combo chance at maximum of 80%. Once you do this, you should be able to set the rock on fire for extended periods of time (If it is not on fire for long periods, recruit more slammers.) Recruit bombers until this achievement unlocks.