AFTER BURNER CLIMAX

This is the easiest solution for the achievement on this site:

Just set "Secret Mission" to "always" in the "EX Options", and make sure you destroy all the missiles in stage 15. That's it.

Background note: The other guides on here are how to do it without "cheating" with this specific ex option, as you normally would not make it to stage 14 and 15 with accomplishing some goals in the previous stages.

EDIT:

DragonYen notes "I did a quick Google search and it appears that the particular EX option you need is unlocked by: Completing 20 Total Emergency Orders". JackX289 verified this.

EDIT 2:

As you can read in the comments below, some cannot catch the last missile as it is faster than your jet. You have to "play it on fast". I forget what this means, but it should be obvious to anyone currently playing the game. Perhaps you have to use afterburners.

EDIT 3:

Big Ell notes that "Completing 20 Total Emergency Orders" unlocks the required EX (read above) is wrong and "you just have to Play 20 Emergency Orders. So just play through the game around 5 times."

Credit to PiaCarrot jawp on his guide. Hopefully this can expand on that and be as comprehensive as possible.

I'd recommend that you go for the other achievements in the game and leave this till last. That way the chances are likely that you'll have most of the EX Options unlocked that will make getting this achievement ALOT easier.

First of all, regarding the 'Secret Mission' EX option: I didn't have this when I got the achievement. Unlocking it requires that you complete 20 Emergency Orders. However, with a select bunch of EX Options, you can complete all of the Emergency Orders in a playthrough required to unlock missions 14 and 15 and get this achievement at the same time.

I used the following:

Credits: 9
Aircraft Count: 9
Lock On: Large Cursor (This one I think is essential!)
Gun Power: Up
Auto Gun: On
Climax Guage Recovery: Free (Again, this one is essential)
Armor: Half Damage
Enemy Attack: 1 Level Down
Display: No Smoke (All)
Aircraft Speed: Normal (Don't adjust this one)

There are undoubtedly others which will make this even easier but this is a good foundation.

Now, onto the Emergency Orders...

Stage 3: When the prototype craft is introduced, immediately begin spamming Climax Mode. Doing this, the craft will slowly come into view and you will have a huge window in which to shoot and unload missiles to destroy it. Easy!

Stage 6: This introduces the Stealth Bomber, which you cannot lock on to for your missiles, the machine gun must be used. Strangely, the first time I completed this, I didn't destroy the bomber in Stage 6, but at the beginning of Stage 7. I think it's possible that if you stay behind it, it will carry on to the next stage. However again if you spam the climax mode and keep as close behind it as possible, Auto Gun will make a pretty easy job of destroying it.

At the end of Stage 7 you get to select out of either Innocent Land (Left) or Forgotten Glory (Right). I went right and selected Forgotten Glory...

Stage 8B: For this you will have to destroy 10 ground troops (Even though they fly about... weird!), which will appear at various points with red TARGET markers above them. Both attempts I've had this, I've killed what I believe to be a maximum of 13, so you do have a window to work with. Again, when they come into view, spam climax mode and use your locked on missiles to take them out.

Stage 11: This can be a little tricky, but again the Free Climax Mode spamming is your friend. You have to finish the stage without being painted by the white searchlights dotted throughout. These are not the same as the red laser beams which will damage you, but they won't ruin your progress for this so bear that in mind. The flashlights can be targetted and destroyed, so decelerate to your lowest possible speed and keep the left trigger held down to keep your speed down. Spam Climax Mode and missiles to take down the searchlights.

You get another choice at the end of Stage 12. I went right to the Nuclear Arsenal.

Stage 13B: This is another prototype craft that must be destroyed, lock ons are allowed. You will come across the craft after going through the first bunker section with the lasers. You will be out in the open the craft will fly infront of you. The usual tactic of spamming climax missiles (I'm trademarking that) will take care of it.

At this point you've cleared the necessary Emergency Orders, and will now progress to stages 14 and 15 instead of finishing the game at the end of 13.

Stages 14 and 15 literally happen in a flash so pay full attention. Stage 14 requires you to destroy three missiles with the gun and that is all. Stage 15 gives you a time limit of 30 seconds to destroy the last missile while under fire from alot of enemies. Spam missiles to take care of the enemies and then use full acceleration to close in on the last missile and shoot it out of the skies!

Congratulations, Ending A will being playing at this point and you will unlock the achievement!

All the best guys, peace! x

Requirement for this achievement:
Clearing all "Emergency Order" to advance your progress to Stage 14 and 15.(If fail one of them, your game is over after Stage 13 and see "Ending C".)
Destroy all missiles in Stage 15.(If you fail, you'll see another ending, "Ending B".)

If you think requirement described above is hard, play some games as usual and turn following "EX Option" on.
Secret Mission: "Always"
Gun Power: "UP"
Auto-Gun: "ON"
"Secret Mission" option leads you to Stage 14 even if you fail "Secret Order", and "Gun Power" and "Auto-Gun" help your attack to missiles.

EDIT: Other "EX Options" give great help, especially unlocking it without "Secret Mission" option. For example recommendation, see Lolatron's guide.

For ENDING A - you need to complete Stage 14 and Stage 15 which means that you need to complete two last Emerging Orders.

If you won't be able to shoot all the missles at the Stage 14, those would be transferred to Stage 15. Be sure to put the pedal to the metal and as soon as you get as close as it gets to the missles, use Climax Mode and aim carefully.

To have ENDING A, you need to complete all emerging orders through the game which can be a pain in the back. The other way to do this is to turn on the special EX option which would allow you to have Stage 14 and 15 always available - even if you won't accomplish any of the emerging orders (but you need to complete those during the Stage 14 and 15 anyway).

To have EX option SECRET MISSION ON you just need to PLAY 20 emerging orders - you don't need to COMPLETE them as it is written in guides above/below. You just need to play them so just play the game couple of times and it will come for sure.

That is the best way because the game takes couple of minutes and you can turn a lot EX options before you will get the one you are interested in so the game should be a piece of cake by then :-]