After Burner Climax

I got this achievement randomly during one of my Arcade Mode playthroughs. To make it easier, use the EX Option "Large Cursor" (unlocked by reaching the ending one time) as well as the EX Option "Combo Window: Long" (although I didn't use the latter, it may help you). During one of the later missions, get as many enemies in your crosshairs at once and blast away with missiles.

For this achievement you need to get a combo of 50 while playing in arcade mode. This may seem impossible at first but it does get easier the more you play the game, the more you play the more EX-options you unlock and they make the game significantly easier.

With EX-options ranging from extra continues to auto lock on the entire game will become infinitely easier the more you unlock. You'll need to complete arcade mode once to unlock the EX-options and once you do so you can select them from the main menu. Doing this will take you to a new menu which will display all the extra options you can activate as well as what you need to do for the others.

Once you've unlocked a few of them and activated them you should be able to get this achievement without even trying, an example of how easy the game becomes can be seen in the video below.

* ^{Credit to Inv4d3rG1r for the video}