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This achievement is for completing the nineteenth mission of the game and can be obtained on any difficulty.
Here's my playthrough of Mission 19 Lighthouse.
Aircraft used: F-22A
Special weapon: 8AAM (8 air to air missiles)
Score required: 12,000 (Normal)
Time limit: First section 9:00 / second section 20:00 (Normal)
This mission starts at the Space Elevator and you are tasked with eliminating enough enemies to reach 12,000 points within 9 mins on normal difficulty. This is isn't too hard as long as you focus on quickly moving from target to target.
Roughly 3-4 mins before the timer runs out, Helios missiles are launched. Pay attention to your radar and avoid the red circles - you have a few seconds so move away quickly if you find yourself caught within one.
The second part of the mission revolves around destroying the Arsenal Bird. Ignore the drones or other aircraft but be mindful of missile locks on your plane. Focus on destroying the propellers and move away when the energy dome is activated. Return to attacking when the dome is down again.
When all of the propellers are destroyed, attack the hooks that become exposed from underneath. They are at the wrong angle for an attack from above but can be hit from below. Finally destroy the APS unit on the Arsenal Bird and the mission is completed, save for an easy carrier landing.
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.