I have finally got that bloody screenshot the hard way, by playing through two fifths of the game until I found it.
Also Balrog isn't a boss. You find him in a hidden room and he mentions that he is lost. After that you can use the character in Free Mode.
This is what you need to do to get Balrog:
1. You need to complete Scenario 1 in its entirety to unlock Scenario 4.
2. In Scenario 4 you need to go to Florius to get the Jump Boots.
3. Go to the the Great Machine and find the Lasso.
4. Still in the Great Machine you must go to the area with the floor switches.
5. Navigate to the bottom-left floor switch. If the floor is missing and you can't reach it then toggle the top-left floor switch first.
6. You should see a wooden post across a gap to the left of the switch. Use the Lasso to cross the gap.
7. You should then lasso across a number of gaps until you come across a 1 tile gap you can't lasso across.
8. Use the Jump Boots to cross the gap.
9. There should be a door up ahead with Balrog inside.
I am sure that no-one here really cares, given how obscure this game is, but given how information on all of this was so scarce, and I went to such lengths to find it, I figured that someone would benefit from me posting this somewhere on the net.