As you should already know, you can safely fall down the elevator shaft to find a hidden room. Once you build the first shortcut a TV will appear on in that room on the second floor. What you need to do is bring that TV all the way from the second floor to the blacksmith on the fifth floor. What makes this hard is that you can't roll with it, the rat will try to steal it and you need to safely toss it across pits. Needless to say, its not fun.
I included the last bit just so you can feel my struggle. I wasn't thrilled my companion killed the caped bullet, but I rather he dies than lose health or worse yet, the TV.
I'll upload some gameplay later. Right now I am hoping this is the run where I beat the sixth floor.