As it turns out, Super Mario 3D World is two games in one. You have Mario's 3D platform adventure, and then there's Luigi Bros. What is Luigi Bros.? It's the original Mario Bros. arcade game from 1983, except both characters are Luigi.
You can unlock Luigi Bros. one of two ways. Beat Super Mario 3D World through World 8, otherwise known as the hard approach, or pick up a copy of New Super Luigi U and record a save file to your Wii U console; quite frankly, you should have done this months ago.
That said, this new Super Mario 3D World video breaks it all down.