The two men will be in opposite dug-outs at the Municipal Stadium in Poznan as their respective teams attempt to launch their Group C campaigns with an opening day victory.
However, the 43-year-old believes he and the veteran Italian, who is 30 years his senior, have done their homework so thoroughly that both know exactly what to expect.
Bilic said: "I follow the Irish team and I know everything about them. They aren't hosting the tournament, they are not playing at home, so they didn't get a wild card to get through the qualifiers.
"They did a great job. They were in a group with Slovakia and Russia, so I respect them.
"They play very good football, but their football is very simple so, objectively, they are not such a heavy team to analyse.
"I don't know how they will play tomorrow. Maybe they will attack us, maybe they will surprise us.
"But they play one way, so I don't know if they can still surprise us - Robbie Keane probably won't be on the bench.
"In the same way, we can't surprise them. We know everything about them and they know everything about us, but we still have some tactical changes and maybe there will be some surprises.
"But we are playing a huge game, a big match and if we play the best we can, we will win, I am sure."
Whatever else he feels about Ireland and the threat they represent to his country's hopes of progression, Bilic has immense respect for Trapattoni and what he has achieved not only in his latest post, but throughout his managerial career.
He said: "What can I say about Trapattoni? Trapattoni is a big coach, he is 'Mr. Calcio'.
"He has worked with Milan, Juventus, the top clubs and not just that, he was still the man even when he was working at Bayern Munich.
"He is famous for his words and he is still famous because he has brought the Irish team to the European Championships. What can I say?"
However, Bilic remains confident his team can get the better of the Republic and pave the way for yet another strong showing at a major tournament.
Croatia have twice reached the quarter-finals of the competition since first taking part in it as an independent nation in 1996, and have been consistently ranked among FIFA's top 10, where they currently occupy eighth place, 10 ahead of tomorrow's opponents.
Bilic said: "In the last five years, we have been constantly in the top 10 teams in the world, which is phenomenal for any country, but especially for our small country.
"But this has not happened just in the last five years. Since we got independence, Croatia has missed only two tournaments and I think after the top seven or eight teams in the world, we are right there.
"We have been among the top 10 teams for about 15 years and we are proud of this and we are respected.
"All our opponents, they are always shocked at how small a country we are."
Three points against Ireland would maintain that record, and while Bilic, like Trapattoni, knows there are perhaps sterner tests to come in the shape of Spain and Italy, he will take nothing for granted.
He said: "We still have to play against Italy and Spain, so we can't focus just on the Irish, but also on Italy and Spain.
"What we have to think about is just to do our best. There are three matches - it's not 13 matches, it's just three and the first match is very important.
"We have to play very well because our nation is full of hope and if we can get three points, everything will be easier.
"As a player, I was in the same situation and it would mean a lot if we could get three points from our first match."
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