Twice World Cup winners Australia have not held the annual trophy contested between the trans-Tasman nations since 2002, and Genia has known only disappointment in his seven campaigns since his 2009 debut against the All Blacks.
Every year has added to the frustration, with last season's defeat especially galling. A last-gasp try by Beauden Barrett denied the Wallabies a breakthrough win in Dunedin and sewed up the series with a game to spare.
"I can only speak from my personal point of view but to me I'd have to say it's the pinnacle," Genia told reporters on Monday, in the leadup to the Rugby Championship and Bledisloe opener in Sydney.
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"I mean, the World Cup is obviously up there but how often do you get to play the best team in the world three times and have to win two out of three to win a trophy?
"I haven't won a World Cup so I'm not going to say it's harder but for me it's the number one priority because as I said, they're the best team in the world for the last 15-20 years, back-to-back World Cup winners.
"For me that makes it incredibly difficult. Also it would make it incredibly special if we're fortunate enough to do it."
Australia broke a seven-match losing streak against Steve Hansen's side in the third and final match of the series in Brisbane last year and will head into the Saturday's opener at the Olympic stadium with some optimism.
The match also doubles as the opener for the southern hemisphere's four-nation Rugby Championship, featuring South Africa and Argentina.
There will be some queries over captain Michael Hooper's fitness, with the flanker having been sidelined with a hamstring injury since June.
But the side had been buoyed by the return of ball-poaching maestro David Pocock, who missed last year's Bledisloe series while taking a sabbatical, said Genia.
"I think the difference he makes you all saw at the World Cup in 2015, one of the best players on the planet," Genia said of the loose forward, who played a big part in the Wallabies' surprise run to the 2015 final in England.
"So he brings what he brings in terms of his ability as a player but as well as driving standards off the field, he drives them on the field."
(Reporting by Ian Ransom in Melbourne; Editing by Greg Stutchbury)
