Swinton, 54, who won an Oscar for Michael Clayton and recently starred in Snowpiercer, plays the part of Dianna, a brassy and crass men's magazine editor in the Amy Schumer comedy.
Dianna, who dishes out backhanded compliments with ease, wears her hair long and curly and isn't afraid of a smoky eye.
"She's kind of pitched herself at that because she thinks that's like the kind of alpha female magazine editor, and that was it really," Swinton told TooFab about her character's look. "That she would be dressed in Victoria Beckham because she kind of aspires to Victoria Beckham's aesthetic and is a train wreck, let's face it! But it's all done very scrupulously; she's trying to look as absolutely alpha as she can."
The actress, who has two children, also opened up about her look in an interview with The Huffington Post, telling the site she's "delighted" to be unrecognizable in the film.
"I don't know whether one would really want to be recognizable in this role," she joked.
The actress told the site that her dramatically different appearance was the result of "a lot of makeup and a kind of tandoori tan." The hair? A wig. "That's all it takes," she said.
"The truth is there are a lot of women walking around rocking Dianna's look, and I suppose you maybe didn't ever expect to see me in it," she told The Huffington Post. "But here we are, and it's available for everybody. You just have to go to a big makeup counter in a big department store and you, too, can get that look."
Swinton told PEOPLE that when it comes to her personal style, she prefers "pure function" over fashion.
"I'm really not that interested in fashion, to be honest, or knowledgeable about it. I tend to wear clothes by my friends and [choose] comfort every time."