If you own Asia at any point in a Devastation Risk game, there are certain things that must be done: fortify Siam if you own Australia, fortify Kamchatka, and make an alliance with the largest power in Europe (they have the most routes to attack you). Make sure your alliance involves consultation, as discussed in the variant rules, so that Europe and North America cannot work together and backstab you.
You should fortify Siam because if you are destroyed you can pull back to a Fortress Australia strategy and try to come back. You can also place armies in Siam and, using the Devastation Risk end-of-turn transfer rules, move as many armies as you want into you Asian countries if a problem develops. This gives you an safe arsenal for emergencies. Australia can only be attacked by Siam so remember not to move all your armies out of it and into the emergency area.
Kamchatka is the only place where North America can attack you. If you have that secure and you have built up a strong army, I say go and attack North America. But make sure you will win and don't move all of your Kamchatka armies into North America, that way, even if you lose in North America they cannot strike your Asian forces. If you have successfully taken Alaska, while maintaining a strong force, and if they only have one man defending each North American country then go ahead and keep attacking. If you started the attack with huge numbers of forces and still have them, go for the big gain and take the continent, just be careful.
Once you have taken Greenland, that alliance with the European player becomes even more useful since they cannot attack through Iceland. This gives you time to deal with South America and build up before you break the alliance and finish off the opposition. They will try to take Greenland and attack Asia once the alliance is broken, but if you fortified enough they won't succeed. Once you have conquered South America, you can break the alliance like discussed above and go for the ten points, or, if you're a more conservative player, you can share your win with Europe and take the five.