R.U.S.E.

Simply win a battle mode on medium or higher during each of the three time periods. You will have done 45 when earning Ace. For 42 you can't face a prototype enemy so I used a regular one. The paratrooper rush won't work so I did the following:

You need to switch to America but keep the AI as America as well. Start off by building an airfield then researching the B17 flying fortress. Build a supply depot. Build an Anson and have it flying a little south of his HQ. Build a B17 and send it to take out the stuff he has built to the southeast of his base. Build 4 paratroopers. Let your B17 resupply then send it towards his base. He will camouflage the sector but you will still take out his airfield and any planes he has on the ground. At the same time send in the paratroopers. Land them right where his HQ is and as soon as you are on the ground you can capture it. Move your other paratroopers around to take any other supply depots or buildings he has (he had an artillery base left for me). He will now only have some planes in the sky, so research the fighter bombers and send them to take out his planes (as they have been unable to land they won't have ammo to fire at you).

For 39 you are not able to build B17's so you have to adapt the above slightly. Start out again by building an airfield and 2 of the B25 bombers. Build a supply base. When both bombers are built send them over to where he has started to build up to the southeast of his HQ. Take out the buildings there. While doing this research paratroopers. As soon as this is complete, send the bombers over his base and attack it. He will camouflage. At the same time send 4 paratroopers and drop them right at his HQ. He will have built some planes but they will focus on your bombers rather than your transport so you will land the paratroopers, capture his base and his airfield and again all he has left is some supply depots and planes in the air.