Her imposing game, force of will and hunger indeed make the American especially difficult to stop at tennis' four major tournaments, evidenced by a winning percentage of 88% at grand slams and 85% in all other top-level main draw encounters.
'When she is in those events is where she really turns it on,' longtime pro Samantha Stosur told CNN.
Williams has, in fact, walked away from a major 39 times without hoisting the trophy but those defeats have been spread over 17 years and it hasn't happened since Wimbledon in 2014, when Alize Cornet sent her packing.
So how, then, does a player oust Williams at this U.S. Open, which starts Monday in New York, and prevent the 33-year-old from becoming the first player since Steffi Graf in 1988 to complete the calendar year grand slam? Russia's Vitalia Diatchenko hopes she has the formula when she plays Williams in the first round as part of Monday's night session.
Producing the proverbial 'match of your life' and benefiting from a subpar Williams -- either physically or other -- is one combination.
Stosur, who holds the distinction of being both the last player to down Williams in a grand slam final and the last player to defeat her at the U.S. Open, both in 2011, said having the requisite amount of belief is key.
Putting away Williams -- and overcoming her aura -- in Sydney in 2009 proved to be an overwhelming proposition for the Aussie. Holding four match points, she double faulted twice and admitted to shaking. Williams prevailed 7-5 in the third set.
'I got really nervous,' Stosur said. 'I thought, 'Oh, my God, I'm going to beat Serena Williams, in Sydney! It's amazing.' Then I missed a volley by five meters and suddenly it was all over. That was definitely a big lesson learned, that if you have the opportunity, you have to play the point and try not to think about who is on the other end.'
Sure enough, when they met six months later in Stanford, Stosur won in a third set. A year later Stosur, who boasts a potent kick serve and heavy forehand, edged Williams in a thriller at the French Open.
The 31-year-old is one of just three players, along with fellow grand slam champions Jennifer Capriati and Justine Henin, to own a winning record against Williams at grand slams with at least two head-to-head matches.
'I have to do a couple of things, especially that match up well against her, that I know have worked well in the past,' the 22nd-ranked Stosur, who has lost eight of 11 matches against Williams overall, said. 'If I can do those, then I know that I can trouble her. And if I don't do those or don't execute it well enough, I know she's got just as many weapons to trouble me and it could be a very different story.'
The lone occasion in 60 matches Williams exited in the first round of a major came three years ago at the French Open, undone by -- rarely -- a lack of killer instinct and an inspired opponent, Virginie Razzano, who was competing in front of her home fans in a predictably partisan environment.
Like Stosur, Razzano thought she could beat Williams. Step one.
Helping matters, in her case, was consulting YouTube in the days prior to the tussle to study Williams' habits.
'I'll admit I didn't sleep well for three days before the match because I was so perturbed to play her, because I really wanted to get past the first round,' Razzano, a flat-hitting baseliner, told CNN. 'I said in my head, 'Psychologically I have to be ready to beat her.'
'Serena is a great champion and very difficult to beat. I couldn't go on court with eyes closed, without a clue.'
Dropping the first set did little to discourage Razzano, she said. She stuck to her tactics and didn't shy away from turning the match into a physical encounter, which is what ultimately transpired.
Williams surrendered a 5-1 lead in a second-set tiebreak, wept in her chair ahead of the final set and looked on as Razzano closed out the three-hour contest 6-3 in the third despite suffering from cramps.
'I felt like I was in a football stadium,' recollected Razzano, who a year earlier played at the French Open shortly after the death of her fiance. 'The fans stomped their feet and clapped their hands at the same time. I thought center court was going to explode. I felt the vibrations.'
The result, though, transformed Williams: She subsequently turned to coach Patrick Mouratoglou and has won eight of the 13 grand slams contested.
But thanking Razzano, who fell in U.S. Open qualifying after missing three months with a stomach injury, wasn't in Williams' immediate plans.
'I think after the loss she was bitter,' said the 32-year-old. 'I saw her one month later at Wimbledon and we crossed paths in the locker room and she looked at me with dark eyes.'
Henin toppled Williams at majors three times alone in 2007. Besides possessing the belief, she said Williams' opponents can't afford a physical dip. The ability to play defense and taking the first opportunity in a rally to pressurize Williams, for Henin, are important.
'But (what's) very hard against her is that even if she's not playing at her best, when she is under pressure she can, especially on her serve, do a fantastic job,' Henin told reporters at the Rogers Cup in Toronto this month.
She flashed back to the 2010 Australian Open final, reliving the pivotal second game of the third set.
With Henin leading 1-0 and holding two break points at 15-40, Williams escaped thanks to her serve, arguably the best the women's game has ever witnessed. She struck an ace, two good first deliveries and a further ace.
She would win the finale 6-4 3-6 6-2.
'It was only her that can do that,' the seven-time grand slam winner said. 'Mentally she is the strongest I had to play. Maybe she's even better today than she was a few years ago. It's amazing.'
Cornet, remarkably, has won three in a row against Williams at the grand slams and WTA events -- though one came via a retirement.
'It feels very special to have such a record against Serena because in my opinion she is the best player of all time and I'm proud that I beat her three times in a row,' the 27th-ranked Cornet, a counter-puncher with a reputation for participating in marathon matches, said in an email. 'It means that I had the level and the right way of playing against her.'
Sabine Lisicki, who defeated Williams at Wimbledon in 2013, didn't return interview requests sent via email, while another competitor who has toppled Williams lately at a major, Garbine Muguruza, was unavailable, said her agent. Muguruza stunned Williams at last year's French Open but lost their rematch in July's Wimbledon final.
Henin doesn't expect Williams to lose at the U.S. Open, saying that 'probably she will do the grand slam this year' and thus also match Graf's record of 22 majors in the Open Era. Cornet, Razzano's compatriot, agreed.
Nothing suggests Henin will be proved wrong. But even if in the current climate it's difficult to envisage Williams being bettered in New York, Razzano, Stosur, Cornet and the Belgian herself -- among others -- have shown it's not an impossible task.
Read: Serena ready for challenge
Read: Williams completes 'Serena Slam'
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