So this isn't that difficult to get but the games physics can be awkward and the hardest thing is to get your swing right to break the walls with your bare hands.
Ok to start, The easiest way I found to break the walls is to face 90 degrees from the wall (side on) and looking diagonally away, strafe towards the wall, jump, land continuing to strafe then just as your close swing your view to look at the wall. Make sure you're only holding the object in the hand closest to the wall as well, this gives the object more inertia.
1st wall (usually broken by using the swinging skip).
Grab the fire extinguisher smash the window and jump out (continuing to hold to fire extinguisher). Walk to the right and smash the wall wit hit.
2nd wall (usually broken by the wrecking ball)
Keep hold of the fire extinguisher from the 1st wall and use the same tactic, should be easy. You can leave the fire extinguisher here now.
3rd wall (usually broken with rubble)
As you enter the room climb the blue scaffolding to your right. There's a bar keeping the doors closed. Grab the bar and lift it (look up). This will cause the rubble to avalanche out (this also pops the achievement 'Avalanche!). Using one of the brown bar that was keeping the door closed break the wall.
4th wall (usually broken with train)
Keep hold of the metal bar that you used to break the 3rd wall and break the 4th wall the same way.
The achievement pops a couple of seconds after you walk through the 4th broken wall. Good luck!
Thanks to SuperLoki for the video - this helps explain