Here's what's worked for a group of people I play with:
1) Play the campaign on Elite first, if you haven't. This unlocks Ace difficulty. On Ace, health regeneration is disabled, but you get a lot of points for it in Free Mission.
2) Play the missions Pipeline and Siege first. You can do these on Elite or Ace and probably get an A, Siege is easier on Ace than Pipeline. I did them both on ace in an F-15E but it's up to you. This unlocks Multirole Pilot, which boosts points when you fly a multirole plane.
3) Equip that, and go back and do the fighter/multirole missions in a multirole. If you want, take the Super Hornet and ECM pods to prevent enemies from hitting you - it's worthwhile on some missions, especially when flying on Ace. The combination of Multirole Pilot + Elite or Ace should get you As on every other jet mission. Just use DFM heavily, take out green enemies before red TGTs and those before red TGT_LEADs to maximize your score. Make sure to get all targets in ASM for bonus points, that kind of thing.
For the door gunner and AC-130 mission, it's just straight memorization. Memorize spawn spots and especially where enemies who fire SAMs are. Remember that both the Black Hawk door gun and the AC-130's 25mm can shoot down incoming missiles. You should be going for quick destruction of as many targets as possible. The door gunner one you should do on Ace, as it's very difficult to get above a B even on Elite.
For the Apache missions, I suggest taking any skills you have that boost your MG damage and cooldown, enhance your rocket launchers, and increase your payload. Then just hit everything hard and fast, and don't get shot down. On the first helicopter mission, take AAMs just to destroy Hinds, because enhanced rocket launchers + enhanced MG can take out pretty much every ground target so you won't need 4AGMs as much. However -- on the second helicopter mission 4AGMs are much more useful for hitting hard targets like tanks, letting you cycle between rockets and 4AGMs to clean up everything very fast. You get a better time bonus and chain kill bonus, which can be critical.
And last tip, for Hurricane, you have to shoot down a significant number of the escorts to get this, but if you try to DFM them all, your targets will escape. Instead, take advantage of their unusual lack of aggression, slow down to about 300 knots and weave back and forth - they'll fly in front of you and you can just missile them.
In general though if you get shot down don't worry too much, just restart from checkpoint. You lose your Armor Bonus, but I've successfully gotten As on several missions after respawning. It's best not to get shot down, of course, but it's not a dealbreaker.
Your reward for all this, besides the achievement, is the Ace skill - increases points earned in any aircraft or helicopter. Worth it, especially if you want to chase after some of the 1,000,000 point unlocks.
Here are some per-mission scores to target. These are the lowest scores anyone on my FL has (including me ) whom I know has an A on every mission, rounded off for easier reading. In general, most missions require 2000-2100 points, but the minimum point total is different from mission to mission.
Nightmare: 1800
Inferno: 2080
Red Moon: 2500
Spooky: 1920
Blue on Blue: 2030
Power Play: 2410 (confirmed that a 1912 will B rank you)
Lock and Load: 1710
Pipeline: 2430
Siege: 2240
Hostile Fleet: 2040
Launch: 1920
Motherland: 2130 (a 2076 was a B rank; almost certain the cutoff is 2100 on the dot for this)
Aftermath: 2020
Home Front: 2200
Hurricane: 1900
Akula: 2140
You may get an A with fewer points than these, but they should give you an idea of what's possible. All of these were on Elite or Ace.