“Welcome to the most controversial show at the Edinburgh Fringe,” says Amanda Knox at the top of her debut standup comedy show . Unlike most newcomers, Knox has not been afforded the space or time to hone her hour-long offering in front of a live crowd: the show sold out ahead of its run and has been the subject of much media scrutiny, with news stories questioning whether it’s appropriate for her to be here and a petition hitting 42,000 signatures calling for it to be cancelled.

Before opening night, Knox has already received enough backlash to send the average solo performer reeling from the limelight in terror, but as she steps onto the stage and gives her morbidly curious audience a little wave, the 39-year-old seems unfazed. After all, this is a woman who has spent her entire adult life being judged by strangers. Aged 20, she and her then boyfriend Raffaele Sollecito were wrongfully convicted of the murder of Knox’s flatmate, Meredith Kercher, and imprisoned in Italy following a trial broadcast all over the world.

The media was viciously obsessed, printing an endless stream of headlines defamatory enough to stain her name for life. Despite being acquitted after four years behind bars, the road to exoneration ate up most of Knox’s twenties (and there are many online who still loudly question her innocence).

It’s this experience she’s here to share with audiences – and it’s not, as claimed by the petition mounted by a friend of Kercher’s sister Stephanie (who also appeared on BBC Breakfast to condemn the show), a performance that “normalises and trivialises violence against women”. Knox’s own ordeal only began after the terrible brutality of Kercher’s death, though she does share an intimate, heartfelt tribute to her friend.

Dressed in a T-shirt in unicorn shades of purple, pink and blue, and leggings splattered in neon splodges, she recounts her trial and the mental scars it’s left her with self-deprecating dark humour. Shifting between dark and light, she’s kooky, warm and markedly unselfconscious. Even once home, she couldn’t go out, find a job, or date, like her friends. She couldn’t “Netflix and chill” either – “I Netflix,” she jokes.

Which raises a point: the ultimate dream of many Fringe attendees would be to have their work adapted for the screen, but Knox is already world-famous, with multiple documentaries, books and a podcast to her name. She doesn’t need to put herself through the gruelling pressure of live performance, or the risks involved in coming face-to-face with a public audience.

So why is she here? What quickly becomes apparent is Knox is a natural on stage with a keen sense of irony. We also get a taste of the former theatre kid she describes being as she breaks into a few tuneful bars of “Maria” from The Sound of Music. There are a few dud lines, like a recurring joke about people having the confidence of a lesbian with a power tool, and cheesy puns on her name, like her getting “Knoxed up”, though the latter segues neatly into a bit about the tabloids running wild with her teenage soccer pitch nickname of “Foxy Knoxy”. For the most part, her standup show is masterfully lucid and hits the right beats.

Knox explains, in her own words, some of the things we’ve heard previously, including the infamous cartwheeling in the police station incident. She did the splits, not a cartwheel, she says – and only when prompted by a guard.

Now a mum of two young children, she delivers her show on a stage dressed like a nursery, while tidying away toys and folding small clothes. How can she encourage her five-year-old daughter Eureka, in particular, to be confident in a world that stripped away her own freedoms?

There is no simple answer to that question, but nor does this performance leave any doubt that Knox – who bravely invites her audience to join her in the bar after the show – is here with a motive other than to find out.

‘Amanda Knox: Cartwheel’ is running at the Edinburgh Festival Fringe to 17 August