Well, this response is way after the fact, but I just played this scenario (as Britain, on Noble) and after a couple of failures, I won. It was a long hard slog. Here's my strategy:
Step 1: Hide your fleet in port and cede naval control of the Med. for the moment. You'll need your battleships for later, when the Germans start flooding the seas with battleships and troop transports. Because of the 25% defense bonus in coastal tiles, it's risky even for a battleship to attack a destroyer.
Build tanks and bombers, push the Italians west, take Benghazi, and build up forces there. This is at a nice bottleneck in the desert where you can control attacking Vichy & Italian forces. The Vichy don't have any oil, so all they send is artillery, which you can kill effectively with light tanks.
Step 2: Reclaim control of the eastern Med. Put your bombers around the coast and in Nicosea. Bombers at Tobruk are very useful, because they can either strike at ships or at land forces attacking Benghazi. Bomb enemy ships down to strength 20 or less before sending out a battleship to finish them off. That'll give you 95% or better chance of victory. In my game, I ended up killing 109 enemy battleships and losing 3. It's pretty easy to grab Crete and station a large naval force there, which will let you blast approaching invasion convoys out of the water long before they get near Egypt.
Step 3: Capture Sicily. I used about 5 transports worth of troops and still barely did it, but once you have Sicily, you can bomb the Italian oil fields, and slam the Italian war machine to a halt. Around now, you may also have spies, which you can use to sabotage the German oil wells.
Step 4: Roll up the Libyan cities, and with the help of your allies, drive through Tunisia to capture Algiers. Now you can leisurely mop up the remainder of Vichy North africa.
Step 5: (optional) invade and take Italy.
Step 6: invade Greece. I landed 11 transports worth of tanks and artillery in the hills south of Athens, and lost most of my tanks in the immediate counter-attack. But plenty of artillery and shuttled-in reinforcements did the trick. Also, De Gaulle had helpfully just captured the southernmost Greek city. Victory by September 1943.
I also tried playing as Vichy France, and that was a lot easier. The main problem is that you start with no oil. However, if you ask the Italians they will very graciously let you use their oil long enough to build a couple of transports worth of tanks and artillery and pop over to capture Gibraltar. Improbably, Gibraltar sits on top of an oil well. Now you can return the oil to the Italians, forget about naval forces entirely (the Germans and Italians will wipe the Mediterranean free of Allied ships), and send your forces rolling down the railroad into Egypt. Victory by September 1942.
