Given Parker's superior size and speed, he will need to keep on the outside, work his jab and look to use combinations to beat the 1.80m Minto.
"He's had a very good camp," Barry said of Parker. "This is the fight that Joseph needed to really motivate him and he's prepared very, very well. This is the best Joseph Parker I've seen since I started working with him in April last year."
Parker's training camp focused on improving his cardiovascular fitness to ensure he will be quick enough to match it with Minto and there's a good chance he will be lighter than the 108kg he fought at when he beat Nascimento.
It wouldn't be boxing without a few mind games and Barry was at it last week as he called for thorough drug testing before the fight as he raised concerns around the improved physical condition of Minto.
The 39-year-old Minto, ranked 12th by the WBO, laughed off the calls, welcomed the testing and said he was ready for the bout after working under Kiwi trainer Chris Martin during his time in New Zealand.
"This is the hardest I've ever worked in my career and I'm just going to be honest with you and tell you the truth because immaturity was what held me back; and ignorance," Minto said.
"It's a sport that you've got to be dedicated to and that goes for discipline with your social life, the food you intake and the way you train."
Minto's WBO Oriental heavyweight title will be on the line in Manukau in two weeks as well as Parker's PABA interim crown.