The key to an honest shootout win on hardcore mode is the radium bomb. The main challenge in hardcore mode is that enemies rebuild as fast as you can so destroy them. The radium bomb destroys a territory and makes it permanently uninhabitable. This allows you to take out regions of enemy strength and have the gains be permanent. For example, if you radium bomb Indonesia and then immediately nuke all of Australia and New Zealand, then no player can ever again settle Indonesia. If you use radium bombs to take out Egypt, East Africa (the horn), South Africa and the Western territory of Africa that connects to Brazil, then you can nuke all of Africa and no player will be able to take it.
It also helps to radium bomb enemy capitals, which prevents them from ever again using their special abilities.
The radium bomb doesn't make victory easy, only possible. You will still get attacked constantly, which requires rapid response on missile defense and also rebuilding lost territories. This is bad enough that I would say there really is no viable turtle strategy on hardcore mode. If you're not constantly expanding and attacking, you've probably already lost.
On the mobile version, the tsar bomba builds quicker and so is more useful. On the PC version it builds so slow as to be basically useless. I think the radium bomb, the damascus burner, and the hypersonic missile are the best three special abilities. The computers are able to use covert ops to good effect, but I never can. Covert ops is the biggest threat to a radium bomb focused strategy and requires urgent radium bombing of enemy capitals.
There's also a glitch where the radium bomb doesn't work if it hits a dead territory that is in the process of being expanded into. Best to only radium bomb territories that are alive.