Note that this is significantly easier with the stealth suit, or at least having the night vision goggles. Also note that this guide includes many italicized and indented instructions as to get moral points which are not necessary to get the achievement, but do help in getting the alternative ending.
Get up and start sneaking.
Walk up to the rail car you just fell out of. From here you have two options to decide from.
Listen to the officer's speech, but don't stand too close, as the soldiers leave soon afterwards.
Recommended: Very carefully jump on the rails to the right and make your way to the pipes and the slanted wall. If you can't do this, just walk down the staircase.
Players that have gone down the stairs should listen to the soldiers talking. Players along the slanted sidewall can try to listen to the soldiers underneath the bridge talking, though most of the time they will not get the moral point, because they are not close enough to hear.
Those walking on the side need only continue alongside the wall until they see a number of slightly illuminated pipes below them. Players that were on the stairs should quickly proceed down the stairs and into the dark walkway, if they haven't already done so. Be very careful of guards.
Players on the platform just have to proceed down the steps from the walkway onto another sheet-metal and wooden one. Players on the wall should fall to the pipes, crouch under the walkway obstructing their path and proceed to the sheet-metal and wooden walkway.
Both paths end up here. Be careful of holes.
Blow out the light ahead of you.
Walk up to a safe place where you can hear the man about to be executed.
Maneuver around the executor or wait for him to pass.
Get to the place where the man was executed and blow out the light.
In the direction that the light was blown out look down past the rails to a series of pipes.
Jump to these and make your way to the bottom of the metro. Be careful around this area as fall means instant death. In general though, follow the arrows.
Once at the bottom, put on your gas-mask and move away from the Communist side. Be careful of floor traps and the searchlight as you proceed to the Nazis.
Ones on the other side of the trench proceed to the large pipe marked by mushrooms. Get in the pipe.
Once in the pipe you are safe. Climb up the ladders. Once you hear the laughter, slow down again.
Climb out of the pipe and into a small room. This dark alcove is just part of the Nazi camp. Wait for any passing guards. Blow out the light and take the arrows if you'd like.
Wait for the guard to return, take off your gas mask if you already haven't.
Pass into the lit hallway, hopefully unnoticed. Note the generator. You can turn this off using the breaker to the side but escape quickly, as this will notify the guards. This is only recommended for those with night vision goggles.
Move up the staircase. At the top blow out the lamp.
In this dark room, wait for the guards to pass by. Watch out for glass on the floor.
When you are ready, pass onto the rails. Stay to the sidebar though, as a railcar will pass by. Hide when it approaches.
Make your way down the rails and shoot out the lights as you go. Eventually you will hear music and see Nazis along with 3 Communist prisoners. Unfortunately you cannot save them.
Move down off the rails (don't take the stairs). When all is clear climb the nearby ladder and blow out the lamp at the top. Continue to climb the ladders.
At the top are a number of rebar wires, wood pallets, and steel girders to make a walkway across the camp. Move across the top carefully.
At the end, once you reach the wall fall down onto the other steel and wood near the rails.
Make a quick move into the tunnel. There may be guards in here so always think of cover.
When all is clear, move deeper into the tunnel and into the maintenance access.
Once inside the large room you can relax, as there are no enemies in this room. Collect everything you'd like and move to the exit door on the other side of the room.
A flash will notify you that you have completed the level correctly. The achievement will be obtained.
The Invisible Man was a science fiction novel by H.G. Wells in which the titular character had turned himself invisible through an experiment. H.G. Wells is also quoted and referenced in the good ending.