The most impressive performance of his six-year professional career was a points victory over Bermane Stiverne to claim the WBC title. His next and most recent fight - a defence against Eric Molina - was anything but impressive.
Molina, considered a journeyman, put up a better than expected performance, and, although he was knocked out in the ninth round, he hurt the 2.01m Wilder.
Parker, ranked 8th in the WBO and 10th in the WBA, doesn't feature on the WBC rankings, but that should change if he beats Tupou at Stadium Southland.
Four belts are on the line - Parker's WBO Oriental and WBA PABA heavyweight belts, plus Tupou's WBO African title, and the vacant Oriental Pacific Boxing Federation heavyweight title. The OPBF is a significant one as the organisation has strong links to the WBC so a victory for Parker would probably put him at No 15 on the WBC rankings.
"Wilder is six foot seven, but he only weighs 99kg and Eric Molina wobbled him," Parker's promoter, Dean Lonergan, said.
Should Parker win - and the 23-year-old will be favoured to against 32-year-old Tupou who has power but not the hand speed or footwork of Parker - he will fight twice more in New Zealand this year and probably in Samoa in January.
The plan is to move him up the rankings until he becomes a mandatory challenger.
Lonergan, of Duco Events, has recently had meetings with broadcasters HBO and Showtime in the United States and both are keen for Parker to fight Stateside next year.
But if those negotiations fall through, Parker will keep fighting in New Zealand, and probably in the regions following the successful trip to Palmerston North for his recent win over Yakup Saglem and what will be a sellout in Invercargill.
Lonergan acknowledged the threat Tupou represented, saying he and Parker's team weren't getting ahead of themselves.
"Jeff Fenech has been training him and we know he's fit. This is his entry into the big time. A defeat for Joe would set us back a long way."
