Speaking at the Karlovy Vary Film Festival, where he’s being feted with lifetime achievement honors, Australian actor Geoffrey Rush says that the prospect of playing Groucho Marx in Oren Moverman’s “Raised Eyebrows” is “scary,” but that he’s always enjoyed the challenge of complex characters.

It is not a biopic, he says of the film – still in development – adapted from the book “Raised Eyebrows: My Years Inside Groucho’s House” by Steve Stoliar, which focuses on the last days of the legendary comic. “I describe it as a tragi-comedy about mortality,” he says. “He’s 83 to 86, at the end of his life. There’s dementia but you never know because with Groucho he would never let you know that he’s forgetting things.”

Mastering the way Groucho Marx spoke is a challenge, Rush admits. “His dialogue is so hard to learn because it’s non sequiturs – you know how he would free-form. There’s that speech in ‘Animal Crackers’ where he rabbits on for ages, nonsense. Then he says, ‘I’ve told you what I know – now you tell me what you know.’ We’re no closer to anything.”

But diving into seemingly unknowable roles is something Rush clearly relishes, he says. “When I first came to Prague to do ‘Les Misérables’ I’d never ever played a policeman. After ‘Shine’ I thought I don’t want to do another piano film. Except I had to ride horses – never again.’

But the challenge of inhabiting a character who seems unknowable is something Rush says he savors, whether it’s Albert Einstein in the TV show “Genius,” Leon Trotsky in “Frida,” the Marquis de Sade in “Quills” or the notorious Captain Barbossa in the “Pirates of the Caribbean” franchise.

Discovering who Lionel Logue was – the speech therapist who coached King George VI – for “The King’s Speech” was rough going, says Rush, until his descendants appeared with photos and his diaries.

“He was quite dapper – he wasn’t an Australian outback guy. He was polished.”

Rich character studies are a specialty for Rush, it seems. “I’ve done a number of biographical films. The pelican in ‘Finding Nemo’ is not a biographical role but he was Australian – that meant a lot to me.”

Rush recalls his mid-career shift at 44, when he transitioned from being a recognized film actor when he did three Australian films in 1994-95, the second of them “Shine.”

Following screenings at the Mill Valley film fest in California, he remembered being spotted by “a real hipster dude” outside an Italian restaurant in New York. “He just went, ‘Hey, loved your movie.’ I’m a Sydney/Melbourne stage actor and a guy in New York, a hipster, went ‘Hey, I love your movie.’ Your movie.”

Rush admits that costume roles are fascinating to him, recalling the outsize hat he was dressed in as Barbossa in “Pirates of the Caribbean: The Curse of the Black Pearl.”

“I think I must never take this off,” he says. “I always think the hat is the character’s brain. The arrogance, the flamboyance, the power – my hat’s bigger than your hat. Very significant.”

The custom-made suit for his character Virgil Oldman, a “very wealthy man” in “The Best Offer” had a similarly intoxicating effect, Rush recalls. “I always say the outline of the costume is a good indicator of a lot about the internal life of the character.”

And a fine piece of costumery should be seen parading, Rush adds. “You know, close ups are very important in a film. But I always think of extreme wide shots, where often nothing significant is happening but you’ve got to see the character full-length. With Barbossa walking down the deck, you think, ‘That’s where you own the ship. That’s a moment of authority.”

Rush’s visit to Karlovy Vary is the first such outing in four years. During that time, he fought and won a defamation case against a Sydney newspaper. He was awarded $1.9 million after the paper printed allegations Rush had behaved inappropriately toward an actress.

Rush declines to discuss the case with Variety, although in an interview with sister title Deadline, he says: “It was bruising for everyone involved, I think, on both sides. It was an overblown and kind of bloated tabloid event [the defamation case] and the court found the result in my favor and I don’t like talking about it.”