I'm writing an essay about heroes and villains and I want to include Darth Vader. The question is whether I need permissions to write about a character? I plan on selling the piece.
Using characters or settings from an original work of fiction, created by fans of that work rather than by its creator, is called fan fiction. You might not be a fan of Star Wars, however, legal issues fan fiction faces are pretty much similar to yours.
As a result, https://en.wikipedia.org/wiki/Fan_fiction#Legality contains some information that might be of interest to you.
In particular, amongst other copyright holders, Lucasfilm Ltd. is notorious for taking legal actions against their fans, which may be relevant in your case:
In 1981, Lucasfilm Ltd. sent out a letter to several fanzine publishers, asserting Lucasfilm's copyright to all Star Wars characters and insisting that no fanzine publish pornography. The letter also alluded to possible legal action that could be taken against fanzines that did not comply.
Making a personal profit out of it increases the odds of getting sued.