Hold Fire, Press Start, Move to Aegis IV, Hold Up, Press Fire.
Blue Javelin
Hold Fire, Press Start, Move to Random, Hold Down, Press Fire.
Dark Sword
Hold Fire, Press Start, Move to Random, Press Fire.
Fairy
Hold Fire and Bomb, Press Start, Move to Random, Hold Down-Right, Press Fire.
Judge Spear
Press Start, Move to Random, Hold Down, Press Start.
Miclus
Hold Fire, Press Start, Move to Random, Hold Down-Right, Press Fire.
Raiden mk-II
Press Start, Move to Random, Hold Right, Press Start.
Raiden mk-II Beta
Hold Fire, Press Start, Move to Random, Hold Right, Press Fire.
Slave
Hold Fire and Bomb, Press Start, Move to any plane/Random, Press Fire and Bomb.
Raiden Fighters 2: Unlock All The Ships
To unlock all the ships, go to the machine's Test Menu. Enter "Game Settings", change everything to 9 on "Shooter1 Coin/Credits" and "Shooter2 Coin/Credits". Also turn On "Free Play". Now exit that menu and go to "I/O Test". Hold the Test and Service button and repeatedly press the 2nd player's Start button. If done right, you should see the "Days of Operation" counter increasing. Set it to over 140. Exit that menu and reset the "Shooter1 Coin/Credits", "Shooter2 Coin/Credits" and "Free Play" if you wish. You can now exit the Test Menu altogether and reboot the machine. If done right, all the ships will be selectable.
Raiden Fighters 2: Unlock The Ending (USA/Europe Version)
Finish the game twice to unlock the ending.
Raiden Fighters 2: Unlock The Real Last Boss (Japanese Version)
To reach the real last boss, you need to achieve a 100% Target Destroy Rate on levels 3 and 6. If done right, you'll face the true last boss (a black ship) after destroying the fake last boss (a base). In the non-Japanese versions you'll always face the true last boss regardless of your performance.
Raiden Fighters: Play as Judge Spear
At the ship selection screen, move over to the Chaser. Press and hold down, which should bring you to the question mark. While still holding down, press either the shoot button or the bomb button. Doing this should allow you to play as the Judge Spear.
Raiden Fighters: Play as Raiden MKII
At the ship selection screen, push down from either the Aegis or the Beast Arrow (do not move to the Chaser). Then move to the Endeavor. From there, press and hold right which should bring you to the question mark. While still holding right, press either the shoot or bomb button, and the Raiden MKII should be selected.
Raiden Fighters: Slave Ship
Select any ship, if the ship is on top, hold up and if the ship is on the bottom, hold down. Then press start + fire button + bomb button at the same time to unlock the Slave ship. The ship's speed depends on what ship you're using.