What does your antagonist want? A strong antagonist will always want something and will do whatever she can to get it. Your antagonist will usually want the same thing as your protagonist---love interest, job, lead role in a movie and so on. Other times, your antagonist might simply want to humiliate your protagonist, like a schoolyard bully. Determine the what and why of your antagonist’s desires.
Are his strengths equal to the protagonist? Is he a strong-arm man or is he an intellect at a major university? Does he have superhuman or supernatural strengths, such as Dracula? Or is he simply manipulative or good at pushing people’s buttons? Whatever your antagonist’s strengths are, make certain they match toe-to-toe with your protagonist.
Does your antagonist have weaknesses? Does she have a fear of heights? Or snakes? Or is she insanely jealous? Insecure? Dracula’s weaknesses are sunlight, crosses and garlic. No matter how powerful a character he is, she can always be undermined by her weaknesses. This keeps your story from being one-sided and prevents your protagonist from becoming a victim.
Does your antagonist have interesting qualities, interests or quirks? Does he like to play the tuba, for instance? Does he have an interest in fine wines? What qualities or physical descriptions does your antagonist have that make him strong or memorable? William Shakespeare’s villain Richard III, in his play of the same name, has a hunchback and lame arm.
Is your antagonist suitably intimidating? A strong antagonist should provide a serious challenge to your protagonist. Make sure she is a real threat. Have her commit actions which show how threatening she is. The antagonist doesn’t necessarily have to be violent (although, depending on the type of story you’re telling, her willingness to use violence will certainly be intimidating). She can be intellectually intimidating, such as an erudite and well-educated college professor. Nurse Ratched, in "One Flew Over the Cuckoo’s Nest," never struck any of the mental patients under her care, but she still cut a pretty intimidating presence because of the power she held over them and the subtle ways she manipulated their psychological problems.