This will be done at the end of Forkstop 2: Part 2.
Make sure you clear all enemies of the area to start, and at that point you will put the prongs to the top level.

After this you will drive the forklift to the walkway, which is the opposite one of what you are trying to take. After this, climb the forklift and then to the walkway.

The corridor will be located at the enemy spawn, start bringing the barrel to the other side of the room near the top. This will be toward the end of the level.

To the left you will see a drawing of a heart, you will drop the barrel on top of the heart drawing. Once you do this a room will open up and the achievement will unlock.