They are the worst...

"Let me tell you a story, kid. We grew up listening to stories that there will always be the evil and the good, the light and the darkness. And from there, comes the old tale of good guys versus bad guys. In fairy tales, the heroes fight the bad guys, but here, on the other hand, the good guys and the bad guys fight the "evil" guys. "
— Elliot Baldwin Woodman in LOTM: Sword of Kings main quote

Public Enemies is nothing but nothing one of the worst types of villain in fiction. As the name says, they are public enemies, in other words, these villains are so extremely cruel, cold and are so depraved that they become enemies of both sides, villains and heroes.  A public enemy is basically a villains that is regarded as the greatest threat of all.

They tend to be very harmful to be targeted as enemies for villains and heroes and often factions of evil and heroic join forces to defeat the public enemy.