Biggest Irreducible Hello World
Keg,  \$3.3 \times 10^{8912898}\$ bytes
...÷⅍+ℤ,(|⅍+)ℤ,(|⅍+)ℤ,(|⅍+)ℤ,(|⅍+)ℤ,⅍+ℤ,⅍+ℤ,⅍+ℤ,(|⅍+)ℤ,(|⅍+)ℤ,(|⅍+)ℤ,(|⅍+)ℤ,⅍+ℤ,

Program as seen in the raw editor

So where that ... is, replace it with \$3.3 * 10^{8912898}\$ 0s. Then, add a ! after those 0s. This splits the number into chunks, divides these chunks by  and outputs them.
I owe a special thanks to @JoKing for helping me generate a truly irreducible score... it took me a while to understand it, but it got there in the end.