The classic Daredevil villain Bullseye has become increasingly popular over the years. He even had his own mini-series. What is it about this villain that allows him to succeed in a book where he is the central focus?

To a certain extent, Bullseye represents the darker desires of those who feel disaffected.   There is a certain audience segment of escapist entertainment that draws a sense of power from what they read. This occurs when excellent writing produces an amazing suspension of disbelief that takes over the audience. For some, reading a decent graphic novel provides a means to step into the costume of the superhero and defeat the demons  inside them. When spider main clobbers the Green Goblin, the reader is experiencing a certain sense of power over the bully that picks on them or, worse, defeating an abusive father.   The power is, however, reserved. Characters such as Spiderman or Batman are known for their emotional maturity despite their many flaws.  They don't brutalize the villains no matter how horrible the villain’s acts maybe

Bullseye is a one of the worst of Marvel’s villains. He is not bound by any code of honor.  He's associate path.  He kills indiscriminately and without mercy or compassion.  Sadly, this is a character that has been tapped into play the hero role in a few story arcs. We must guess the question why?  What is it about characters such as Bullseye, Venom, The Fool Killer, etc that makes them popular with a certain segment of the audience?

To a degree, these characters represent much of the anger present in the hearts of a segment of the audience.  And they want to lash out any long in the event these feelings through the actions of thoroughly unredeemable characters.

Yes, the context in which these villains commit mayhem is shifted to make those who feel the brunt of the violence deserved of it. This makes their brutal actions seemingly less brutal. However, it is not "less brutal". It is violent, immature rage that provides no answers to the questions the audience seeks. There is no solace there.