1. Research nukes and get anykind of strategic bomber.
2. Get a demagogue of preferred ideology (make sure you do this when you either have nukes or are anticipating to get them while the demagogue does his job to seize the memes of reproduction)
3. When you are ready, let your demagogue start a revolution/civil war for power.
4. Drop nukes wherever you see fit on your core territories.
5. Don't get tried for war crimes by pressing Alt+F4 after you get the achievement.
6. ???
7. Profit.
8. Comment on this guide "Thanks, Ajaxe, you're a good demagogue. I have successfully commited genocide on my own emus in the name of Australia." to let me know you succ'eeded.
9. If instructions were unclear and you got your schlong stuck in a toaster or your local ventilation shaft, or whatever else you found attractive at the time, feel free to ask someone here to send help.

I will not go too much in-depth on achieving this, I can't see anyone bothering to read that either, because I gave the easiest way of achieving this achievement. You can do this if you have enemies on your core territories too, but who wishes to bother with that, when it's just so much more simple to start a civil war, ay?

Have fun committing war crimes and getting away with it.

Fine.

There's really nothing much to it, it's pretty obvious, especially now that I explained it in the shorter version above, it involves you just setting the speed to 5 and waiting it out.
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I did this starting from the 1936 scenario (although you will certainly be able to research nuclear technology quicker by starting in 1939).

To speed up your research process, you need to:
1. Do all the focuses that boost your research (Nuclear Effort and Secret Weapons) and use them on your nuclear research.
2. Set your Industrial Concern to "Electronics Company" (Electronics Concern).
3. Research Computing Machines.

I suggest not doing a Nuclear Bomb Rush™© straight away as you could certainly use some research for your industry to be able to build Nuclear Reactors faster when you research them. I recommend to only start Nuclear Bomb Rush™© when you complete at least one of the focuses that boost your nuclear research (step 1), that way you get some sort of start for your industry.

Once you research Nuclear Reactor, the more of them you build, the faster you will make nukes (production of them begins only when you research Nuclear Bombs).

At some point you need to research a strategic bomber and have at least one to be able to drop nukes, so you must get some production working on creating at least one of these bombers. Along with that, you need some fighter planes for air superiority, although it shouldn't be a problem as, chances are, your enemies in the civil war will not have any planes, but if they would get them, make sure you have some in reserves just in case. Also, don't build Anti-Air in any of your territories to not hinder yourself when you need to drop bombs, in case the territory with the AA emplacements goes to the opposition.

It is up to you to decide when to get a demagogue of certain ideology, but you need him to do his magic to eventually get an event that can start a civil war. You should only start it when you have nukes, just to be safe. Once the civil war starts all that is left for you to do is choose a province where you want to drop a nuke (while having air superiority) and you will officially be one of the weapons of the Third Emu War.