To unlock all of these stuff you have to beat certain bosses to get them and some of them are games you played in the main game but you just play them instead of switching games all the time B&w pocket rush is the first game you encounter when you play but slightly different, Color pocket rush is a color/wide screen/3D version of B&w pocket rush, Combat rush is the fighting part of the game, Master* is hard mode, and in hardcore mode you no longer gain lifes every level and removes the ability to continue after you lose all your lifes.

Mode	How to unlock
B&W pocket rush	After you Beat the tall guy in red for the first time
Color pocket rush	After you Beat the tall guy in red for the second time
Combat rush	After you Beat the tall guy in red for the third time
Hardcore mode	Beat the game
Master*	Beat the game