The annual Scandinavian Days parade in this little north-central Iowa town had barely started when Carly Fiorina fell to the back. Before long, she trailed the high school marching band, the Boy Scouts, the antique cars, several tractors and a miniature van powered by natural gas. Her own float, an Iowa GOP truck trailer blasting Journey’s “Don’t Stop Believin’,” could no longer be seen or heard.

But that was just another opportunity for the former Hewlett-Packard CEO to come from behind. Adversity and bad luck tend to drive Fiorina, and she has suffered more of both in the past decade than many see in a lifetime. Fired from her CEO job in 2005, she decided to launch a 2010 California U.S. Senate campaign a day after a doctor told her she had breast cancer. Months later, her drug-addicted adult stepdaughter Lori Ann died alone in her New Jersey apartment. Fiorina campaigned through the mourning and chemotherapy only to lose by 1 million votes. As Fiorina put it to her best friend and campaign manager at the time, Deborah Bowker, the morning after Election Day, “What were we thinking?”

Then Fiorina decided to aim higher–for the White House. When she signaled her intent to get into the race six months ago, few took her seriously. Now she is getting second looks, partly for her biting criticism of the only other woman running, Hillary Clinton.

Certainly, the parade snafu didn’t daunt her. “We’ve lost our group,” Fiorina, 60, called to an aide. Then she started to sprint, across lawns and through crowds of children hoarding candy and seniors in picnic chairs. At one point she hopped onto the running board of a John Deere for half a block, stopping to greet another potential voter while urging her supporters on. “Oh, Jenna, you’re just showing off now,” Fiorina called to one preteen volunteer who ran ahead to pass out more candy bars.

Fiorina ought to know. Her onstage verve has made her an unexpected early star of the GOP campaign, where she regularly gets the loudest ovations after delivering the most rousing speeches with the sharpest one-liners. But there is another, far more personal, side to her crusade. She is billing herself as someone who understands the darker side of life. She argues that her experience with personal setbacks is a quality that voters should be shopping for in a leader. “It is the flat look of hopelessness,” Fiorina will say, describing what she saw in her stepdaughter’s eyes before she died. “But it’s not just addiction or death that wastes potential. I see that look in too many Americans’ eyes now.”

This pitch sets her apart from the rest of the Republicans in the field, who seek to trade up on successful careers as politicians and celebrities with folksy stories and bravado. Ask her how she explains her drive to work longer hours against greater odds and she will challenge your premise. “The way you’re asking the question, which is the way most people have asked the question, implies that campaigning is hard,” she tells TIME during a sit-down interview in Ames, Iowa, before the parade. “And it is in many ways, but compared to what I’ve been through, it wasn’t hard. It was a joy in many ways.”

Those who know her best put it a different way. “Redemption for Carly Fiorina–that’s kind of the key to her life,” says a former adviser. “Losing a Senate race, getting cancer, losing a daughter. Those are really important, but not as important as redemption.”

To be sure, Fiorina has never been one to shy from a fight. Born in Austin to a judge and an artist, Fiorina was a law-school dropout and secretary before beginning a business career. The first female CEO to lead a Fortune 20 company, she powered up the corporate ladder despite the sexist taunts of colleagues and a memorable business meeting she once had to attend at a strip club called the Board Room. The experiences only sharpened her determination.

And her willingness to attack first. On the Democratic front runner, she can be withering. “Mrs. Clinton, please name an accomplishment,” Fiorina will thunder before Republican crowds, who cheer wildly. “Like Mrs. Clinton, I too have traveled the globe. Unlike Mrs. Clinton, I know that flying is an activity, not an accomplishment.”

So what are Fiorina’s accomplishments? “I certainly talk about my record at Hewlett-Packard,” she tells TIME. “The numbers are undeniable.” Fiorina likes to say she doubled revenue at the company during her tenure, increased the number of patents and increased overall employment. Her critics note that the company grew because she oversaw a massive merger with Compaq, which also led to the layoffs of 30,000 people and a stock price that nearly halved during her tenure.

In a similar vein, she now describes her California Senate loss as a victory of sorts. “I won more Republican votes, more Democratic votes and more independent votes than virtually anyone else running at any point in that cycle,” she has said, a fact that reflects little more than California’s size. Left unmentioned is the campaign turmoil that left many staff bitter, as she let $500,000 in unpaid bills linger for four years, despite a net worth that currently stands at $59 million. “I didn’t owe the money. The campaign owed the money,” she says, sternly. “It’s a closed story.”

Other struggles defy spin. During the Senate race, Fiorina never spoke about the death of Lori Ann, whom she had raised from childhood. Lori Ann had struggled for years with prescription-drug addiction and died under circumstances Fiorina still does not discuss. “It was very raw,” she says. She’s a supporter of decriminalizing drug use and calls for reform of patient-privacy laws to allow family members to interact with addicts’ doctors. “I don’t dwell on it, but I mention it,” she says. “And every place I go, someone will come up to me and say, ‘That happened to me.'”

In only her second month of official campaigning, Fiorina is now fighting a far more circumscribed battle. While a handful of Republican candidates are polling in the double digits in states like Iowa and New Hampshire, Fiorina is jockeying inside the second tier of also-rans like Donald Trump, Rick Perry and Rick Santorum, who are hoping to raise their national poll numbers from under the margin of error. Only the top 10 polling candidates in the field of at least 16 will be invited to the opening Fox News debate on Aug. 6. Despite the positive reviews, Fiorina does not yet make the cut. But she also does not entertain the possibility of failure. “I’ll be on the debate stage,” she says, when asked if she will abandon the campaign if she fails. “I’ll be on the debate stage.”

Fiorina has put messaging–and earning headlines–over building a grassroots organization, a testament to the shifting priorities in a debate-centric contest. Her Hawkeye State chairman, former Iowa house speaker Christopher Rants, started work only on June 6. The bulk of the pro-Fiorina effort has been left to Carly for America, her super PAC, which has so far put only 11 field staffers on the ground in the first three voting states.

Even if she gains the stage, Fiorina’s tiny chance of being the Republican nominee in such a strong field is unlikely to change. What will change is her ability to influence the GOP race, and potentially the general election, when Democrats are expected to nominate Clinton. Her ability to take the fight to Clinton could put her on the short list for any nominee’s running mate. Which means Fiorina is again worth watching, no matter where she ends up in the parade. “Only a woman could attack a woman the way she’s been doing it,” explains one senior adviser to a rival campaign, admiringly.

–With reporting by TESSA BERENSON/WASHINGTON

Contact us at editors@time.com.

This appears in the June 22, 2015 issue of TIME.

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