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This achievement is for completing the eighteenth mission of the game and can be obtained on any difficulty.
Here's my playthrough of Mission 18 Lost Kingdom.
Aircraft used: F-22A
Special weapon: 8AAM (8 air to air missiles)
Score required: None
Time limit: First section 20:00 / second section 15:00 (Normal)
The goal here is to neutralise the air defences around Shilage castle. All targets in the area are hostile so feel free to engage contacts at will. When you have destroyed enough, Sol squadron will launch. Down two of those planes for the second section to start.
Mister X will appear after a cut scene and then you need to shoot him down to complete the mission.
Tip: I played through a couple of hours of multiplayer, gaining enough MRP (in game currency) to purchase the F-15E which made this a lot easier and more fun than the starting F-16C. Around Mission 12, I had enough to purchase the F-22A which is the most capable aircraft I've found so far. The currency, planes and most part upgrade unlocks work across multiplayer / singleplayer but some upgrades are exclusive to multiplayer. You can also go into 'Free Mission' to replay for some extra cash.