Special Mission One: This is accessed from Mission two. About halfway through the level, there are five "towers." Blast the green towers on the sides, then go for the red one in the middle. If done right, a different path will open up, and you will go to Special Mission One after completing the level!
Special Mission Two: This one is accessed from Mission three. Just a bit into the level, seven ships will appear, one will be red, the rest will be green. Wait for the green ones to back off, then quickly destroy the red one! If it has been done correctly, you'll take a new route to Special Mission Two!
Special Mission Three: On Mission four, go about halfway through the level until for green ships appear. Do not shoot them! Instead, wait for them to scamper off, and for five red ships to appear. Don't let them get away! Defeat them all!(I usually have to use an Ex-Arm to do it.) The course will again change, and you will get to play Special Mission Three! If you have played the original Star Soldier for the NES, then this should look rather familiar!
By getting the course changes, you can skip over the boss of that Mission, and you get 10,000,000 bonus points for changing course, too!