Start Alien Soldier and once you're on the main menu, press 'Game Start'. On the next screen, you have a choice of 6 weapons. Select any 4 different weapons and keep pressing start to begin the game.
To shoot your selected weapon, press (B) and then to swap press (A) and then 'Right' to swap them. Press the (A) button to select a new weapon, then press (B) to fire.
Do it twice more to finish it off.