To earn this achievement the enemy killed must be standing still and not running to another tile when they are killed. This can make things difficult as enemy crew almost always run from a burning room if it's occupied by hostile personnel.
This achievement can be achieved most easily while fighting the Rebel Flagship. Simply ignite one of the manned weapons rooms and teleport a Rockman or two into the room before the enemy crew member can extinguish the blaze. Since they can neither run away nor extinguish the fire, this will cook them rather sufficiently.
Alternatively, if you manage to get a Crystal crewmember, you can use their lockdown ability to prevent the enemies from running out of the fire. This works best if you also teleport a mantis or rockman and there is only one enemy so you can finish the fight quickly. Be careful, because crystal crew are NOT fireproof.
Hacking a room locks its doors, so this can be useful to keep crew inside the room while they burn - especially if the enemy ship has upgraded doors, which take longer to blast open. It is especially helpful if you have some kind of stun bomb. This way the enemy can't even try to escape.
Another method, if you have a fire beam send Rock crewmembers to fight on the enemy ship. Just before they kill an enemy, fire the beam at the room they are in.
Funnily enough, this achievement can be gained by killing a Rockman in a burning room. It is much easier than the other races, since they do not flee from fire at low HP anymore as of the advanced edition. All other races will flee from a burning room at low HP, regardless of whether there are boarders in it or not.
This achievement can also be earned by a mind controlled enemy crew member killing a burning crewmate on-board their own ship.
Other Rock Cruiser Achievements: