The tattoo Ardern wants is a photo of the crew of the Endurance dragging the James Caird lifeboat across the ice in a desperate bid to get to South Georgia Island after their ship broke up. The trouble is it would have to be a very large tattoo to get it all in.
"That's survival under the most extraordinary of circumstances. I find that whole period when people were throwing themselves into the complete unknown, the most dangerous of circumstances just to be the first.
"And they thought the thing they were going to achieve and that leadership was all about was achieving the goal of crossing the pole. But actually the story of survival and camaraderie ended up being the much bigger story."
We are in a cafe in Ardern's Mt Albert electorate - the cafe frequented by Ardern and her team of campaign doorknockers.
The pots of tea have knitted cosies on them - one is in the shape of a flamingo.
A Crown limo has driven us to the cafe and although it is Ardern who qualifies for the limo, she is now squashed in the middle seat in the back having lost the game of shotgun.
Such things are taking some getting used to - she is more used to banging around in her old Mazda or partner Clarke Gayford's Holden Rodeo.
Ardern inherited the Mt Albert seat from David Shearer who inherited it from Helen Clark. All three were Labour leaders.
"Something in the water? I don't know."
Ardern worked for Clark, so Clark is an obvious model for her own leadership.
"I can't help but reflect on the way she did the job, but I have to say sometimes all you've got in this job is your instincts. So I'm definitely going to be my own kind of leader."
It is Wednesday afternoon, just after Ardern's environmental policy launch - the second policy announcement of her leadership.
Ardern hasn't had the time to monitor her Twitter mentions but Royal has done it for her.
She tells Ardern she has been compared to "the best character" in Game of Thrones - Daenerys the mother of dragons.
"She just used a dragon to fry hundreds of people," I point out.
"Yes, before that," Royal rectifies. "The bit when you freed the slaves."
Royal and Ardern have been friends for nine years. They met in a carpark during a campaign on homelessness.
Ardern's parents and sister are overseas, and Gayford was in Australia filming. Her friends have stepped into the breach - variously turning into Ardern's housekeepers and campaign helpers. One even made her bed: "That was a bit embarrassing."
"They've travelled with me, spent time with me, one even came and did my bloody washing," Ardern says.
Royal dropped off soup for the freezer but has extra benefits - she is an ad creative and therefore handy when it comes to completely overhauling a campaign in the space of a few days.
If you want to annoy Ardern, sit behind her in a movie theatre and eat some chips. It is her pet peeve.
"Chips in movie theatres. Ice cream wrappers in movie theatres. I have such a visceral reaction to it. It really bothers me. I hate it."
Ardern is a worry wart and says her own worst habit is she is "quite obsessive".
"I think things over a lot. It can get annoying for my family and friends that I constantly want to talk about the thing that is on my mind."
It doesn't take a genius to work out what that might be right now.
Royal was at Ardern's house with another friend the night before Andrew Little stood down and Ardern became leader. It was the night Ardern had to decide if she was willing to take on the job she had always said she didn't want.
They were supposed to be out for dinner for a belated celebration of Ardern's 37th birthday, but Ardern moved that to home once it became clear Labour needed a plan B should Little decide to go.
"We were eating chicken and drinking cups of tea. Chatting, playing out the possible scenarios and talking about how much of a whirlwind it all was," Ardern says.
Royal had expected Ardern to consult on whether she should agree to do the job.
"But she was really clear," says Royal. "If that was what was going to be asked of her the next day, she was ready."
We leave the cafe and a woman passing outside says to Ardern 'Oh, you look just like your picture."
"Thank you," Ardern replies and then frets that might not necessarily have been a compliment, although of course it was.
Just as John Key's upbringing in a state house by a solo mum proved a valuable back story to blunt common perceptions of National, so Ardern's upbringing in a rural area is valuable for a Labour leader.
Earlier in the day she had highlighted her plans for cleaner rivers by speaking of swimming in a local river when the main concern was eels rather than pollution. In defending Labour's plans to start charging royalties for water - including water used by farmers and orchardists for irrigation - she cited her own family background to try to reassure those sectors she would not bankrupt them.
As a child, Ardern was a walking workplace hazard.
She nearly ran over her father in a tractor while learning to drive. She has a scar running down the side of her nose where she was sliced by a piece of farm equipment while running around the orchard packhouse.
At school, her worst subject was physical education. She hated cross country in particular. She wagged school on those days.
She wasn't very good at wagging. She went home to miss cross country once but felt sorry for her friends so put water by her letterbox for them to drink when they ran past.
She did not register that teachers would also be running past it. "My English teacher figured out that must mean I'd wagged. I didn't really think that one through."
Her best subjects were history and metalwork.
"I topped metalwork. I loved the lathe and a good pop riveter. I loved metalwork. But I was the only girl in my class from memory, so they weren't great fans of me taking out the top prize."
She still has that practical bent. She and Gayford got into trouble with the Plumbers Gasfitters and Drainlayers Board for installing their own toilet and boasting about it to a women's magazine, not realising it was not allowed.
"I became a poster girl. They used that story for an ad to notify people about their obligations under the Act when it came to installing toilets."
Nonetheless, legalising toilet installations will not be one of the priorities of her first 100 Days, should she be Prime Minister.