Double Dragon isn't a terribly long game, but you only gt three lives to work with, and that makes it somewhat of a feat when you finally do get to the last boss (spoiler alert, I guess).
But what might not be obvious (at least it wasn't obvious when I first played this stage) is that where the blue stuff is on the bottom of the screen is the wall of whatever building you're in, and there's no rail there, so stray too far down there and
You dead.
So you might want to stay up in the top 80% of the screen just to be on the safe side.