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Current holders Riders are on a 15-game winning run and have won the last 15 meetings between the sides.
Raiders are in transition, searching for their first silverware since winning the competition in 2007.
"Of course they're going to feel the pressure - they know what they're up against," Barber Jr told BBC Sport.
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"We're hungry. I like being the underdog - it's fine, it's perfect."
Though Plymouth have a wretched record against their opponents, American Barber Jr, 31, had success against Leicester last season for former club Sheffield, who beat them to the 2015-16 BBL Championship.
"I feel people are trying to make UK basketball bigger, like with the BBC Sport coverage - I think that's huge," added Barber Jr.
"I'm here to do the impossible. I see what we're doing mentally and I feel that us believing it and knowing we could win, is what's going to help us win."
The final is being held in Glasgow on Sunday alongside the women's equivalent, which Riders are also competing in, with both games being shown live on the BBC Sport website.
Leicester have lifted silverware in three of the past four seasons and sit top of the league table, while Raiders are down in sixth.
"We have played 28 games this season so far and have won 25," said Riders head coach Rob Paternostro.
"It will be a little different when we get there with the bright lights and atmosphere, but when the ball is tipped it will be pretty similar.
"We have a lot of guys who have played in these type of games before in our league and around the world. It's all about the day, and who comes up big when the lights are on."
Plymouth Raiders forward John Barber Jr says they aim to "do the impossible" by defeating heavy favourites Leicester Riders in the BBL Trophy final.