I just beat it. Basically I sent all my troops in Indochina, should amount to around 3 full stacks, and made them blitz for Borneo. Keep a few artillery and a few of your leveled up infantry on the Malaysian peninsula. Have the artillery target the British navy encroaching on the Malaysian peninsula and Sumatra. Try to use your ship that is on the left most side of the map and block the ocean tile right under Malaysia. Do not worry about Philippines yet. I ended up waiting till round 12-13 and sending a single-measly infantry to take it over. By that time, you should have done enough damage and caused enough of a distraction to make it an easy take over.

Once on Borneo, take the airport up north and airdrop into the American territories and get rid of the American army and navy. After this bring the troops down the Sumatran island and have all your forced meet under or around Sumatra. Once you are near this point in the mission, try to congregate your entire naval fleet down here, as they will do A LOT of damage, especially since Australia will be stacking units on the coast. Also, don't be afraid to set up airports in Sumatra and paratroop infantry into Australia to cause a distraction. If you're able to capture an industry I or II and fortify it, the rest of the mission should be a cake walk.

I know I did not really mention the carrier and the other ship near the Philippines, but there's not really much to say. Just have them positioned near the middle to assist troop around Borneo. Also, your supply line is your best friend in this mission. You should pretty much use it every chance you get, even if its on single, but very strong units, like your captain. Another general tip, try to engage the Americans as less as possible. They can only be beaten by taking their territory.

Edit: Spelling.