This is a very simply achievement, the solution can be found by looking at the achievement picture, but I have created a quick video to simplify things.
At the beginning of "It's Getting Hot in Here" you are faced with large lakes of fire that normally need to be put out with rain clouds in order to advance through the level. Instead, draw a bit of armour and go North to a small alcove of rock. You will see a control panel on the other side. Draw fire all over the line of rocks here, and you should blow up some hidden sticks of dynamite. The achievement popped for me immediately after blowing up the rocks, so it appears you do not have to actually use the lift.