This question asks: Why did Darth Vader choose to take shots from Han Solo?
I want to know, why did Han shoot first? Did he even know that the mysterious black armour clad figure was a villain? Or was he still using his cold-blooded instincts as he did against Greedo?
Well at the end of "A New Hope" Han like Luke saw Vader kill Obi-Wan so when he sees this same figure again he thinks I can't beat this guy with a blade so might as well shoot him. I think this split-second reaction has everything to do with his years of being a smuggler when you see someone who means you harm you shoot first and ask questions later.
Edit: I found this link to the the fight between Vader and Kenobi you see at about the 3 minute mark that Han and Luke start shooting at the Storm troopers that were watching Vader's fight. You also see Han telling Luke to shoot the door as he can see reinforcements coming down the hallway including Vader.
Vader was a figure head and chief boogie man of the Emperor. Everyone knew of him... I suspect some doubted his existence and more doubted his powers until they found themselves unable to breathe.
That said his armor was quite similar to that of the storm-troopers. So even if Han did not see him before the fact that he was accompanied by storm-troopers, and looked similar, was probably a good clue that he was a bad guy.
Also, Han was a member of the Imperial Navy. He saved Chewbacca from slavery. He was discharged from the military and went into smuggling. While I do not recall him knowing who Darth Vader was in the books, I would assume that the Sith Lords would have been at least identifiable by their military.
I'd have expected Vader to be pretty infamous.
Perhaps Han didn't recognise him immediately, but when prompted realised that this guy was the black-clad Imperial assassin who's fond of swords that he'd heard about from other smugglers some years back. He'd never paid much attention to that idea, since most of the Imperials he'd ever met were boorish bureaucratic slugs.
