The best thing to do in this scenario is to ignore the goal until later in the game. Start by establishing a strong presence in the world.
First, place all your troops in China. Attack Siam and make a surge attack to Indonesia. If all goes well, you won’t lose very many troops.
Then split your troops in attacking New Guinea, Western Australia, and the Philippines – your goal is to conquer all of Australia by the end of next turn.
Now, have New Guinea and Western Australia both attack Eastern Australia, and make a surge attack to New Zealand. Australia should be yours.
I was lucky enough to be able to trade cards on my next turn. I don’t like that purple has most of Europe, so I will try to take Ukraine. I also want to break into Africa, and expand my presence in Asia.
I make a mistake in attacking the Falkland Islands instead of Peru or Brazil. I lose too many troops and I am left with a minimal presence in South America. Luckily, I annihilate blue; even if I lose the game, I will continue to the next round.
I do my best to surround Ural and Kamchatka, but Ural’s defenses prove to be too strong for me, and two troops from Kamchatka escape to Japan. I’m starting to lose my grip on Asia; I feel a bit overwhelmed.
I decide to take an “all-or-nothing” approach in Africa so I trade cards and reinforce it as much as possible. This doesn’t work as well as I’d like it too, but yellow’s large army of 18 troops is out of Asia and I am now in Europe.
I trade cards again and have a pretty successful turn.
Now I am in control again. I am in a strong position in South America with 8 troops in Argentina; I have most of Europe and most of Asia, and no other player controls a continent. Winning is only a matter of time.
I have conquered Asia (finally) and all of Europe except Svalbard. I have Afghanistan and Indonesia. The only territories that I need to win are Svalbard and Alaska, and to maintain control of Europe.
Alas, yellow makes it into Europe on a surge attack! Perhaps, with the extra turn this provided, I can annihilate him and score a few more points in the tournament.
I retake Europe but am unable to kill yellow. Oh well. Victory.