This achievement is for completing the eleventh mission of the game and can be obtained on any difficulty.
Here's my playthrough of Mission 11 - Fleet Destruction on normal.
Aircraft used: F-15E
Special weapon: 6AAM (6 air to air missiles)
Score required: 25,000 (Normal)
Time limit: 15:00 (Normal)
This appears more difficult than it is, you just need to be quick and hit the right targets rather than trying to get everything.
First head north-west over the mountains to a cluster of oil rigs and ships. Take shots at the rigs and tankers to start with. After a minute or two one your wingmen, Cyclops 1 Wiseman, will state "I went for the structural reinforcements. They're small but not impossible to hit." After that you can target the rig cores - focus on these. Don't worry about anything else and try to be as quick as you can.
Once the rigs are down in the first area, head to the northern most cluster of enemies on your map (in the centre). This is another set of rigs, ships and aircraft. Repeat the previous strategy of going for the rig cores and then mop up as necessary to achieve the required 25,000 score. I ended up with 32,000 so it's not too hard when you know what you need to go for.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.