How to get the American Territory achievement?
American Territory is generally considered one of the hardest achievements in Victoria 3. It requires you to start as the Indian Territories, a sparsely-populated puppet comprising most of Oklahoma which will soon be enclaved by the United States, and to turn the tables and cut the United States down to three states and make them your subject. As the USA is typically one of the most powerful nations in the game, and the Indian Territories are one of the weakest, this is a tall order. However, it is possible to do this with some luck and careful planning.
Ideally, set the game rules to less aggressive AIs. This does not disable achievements and makes eases the risk of the US conquering too much territory or someone deciding to eat you.
The first RNG task is ensuring you can get Texas and thus sulfur, a coastline, and much-needed people. So Texas has to win the Texas Revolution and not get attacked until you can get the US to raise your autonomy. Then you have to conquer Texas (though you will not have any army, so you will need the US to really do the fighting).
Once you have Texas, it slows down. You basically need to just suck up to the US for the next few decades. Get them to help you with your technology and build some buildings in you but don’t let your liberty desire get too low. If they’re nice, they will give you the rest of Oklahoma too. Essentially you are waiting for two things: the Civil War and a power benefactor. Generally it is easy to get Mexico and the CSA to guarantee your independence, but the USA is strong, and you typically you will need someone else to help you. The best bet is to get the UK to guarantee you, as they are usually the only European power that cares about the US, but Austria and France are arguably better if you can get them to help you.
The really annoying part here is that probably about 60% of the time, the US will just not have a civil war. The people will be content to just have slavery forever. This achievement is virtually impossible in that case and you will need to restart. If you are lucky, the US will have a civil war and the Confederates will win. This is good because it means that the US will be substantially weaker, have a narrow connection to their capital, and you will have another powerful ally in the region.
Once you get enough support to outnumber the Americans, declare your independence and add conquering New York and Pennsylvania to your war goals. As long as you can hold your capital, you should be able to win the war without much trouble and probably bankrupt the US in the process. Taking New York and Pennsylvania will instantly make you a recognized power, finally give you enough people to start playing the game, and really hurt the US. You take like 10% of its people, 30% of its industry, and literally all of its iron production. Plus, it cuts off their capital, so you cause mass starvation in DC and no trade anywhere else. It should honestly drop the US’s GDP per capita to lower than African natives’ for the rest of the game.
While New York and Pennsylvania were key for the US, they are less useful to you. Their technology and therefore PMs will revert, companies will be destroyed, and they probably have too many government buildings for you to pay for, so you may consider demolishing their construction sectors and some universities and admin buildings. Despite the states’ infrastructure, you probably still won’t be doing great economically. Once your truce is up, you really want to take Colorado with your benefactors’ help and build up its gold mines. This is key to funding your whole country until you catch up in tech and industry and get a decent tax law.
From then on out it is a fairly typical run. During one of America’s many incoming revolutions and bankruptcies are ideal times to conquer as they should drop to an insignificant power and therefore cost less prestige. Just be wary of a revolution firing during a war as it will take away some of your war goals.
It is important to note though that you don’t necessarily have to grow a ton stronger and conquer the US as much as you just need to demolish them. So while you should be utilizing your infamy, you really want to release New England, Oregon, Apache, Michigan, and anyone else you can. Give states to Mexico as war goals instead. Eating the whole US is like 1000 infamy, so reducing their number of states by whatever other means you can is ideal. Also, a lot of the Great Plains states are homelands of Siouan culture, so they’re a little less infamy to take than out east.
Also suddenly filling the Indian Territories with many times more Yankees than Cherokees or Sioux can easily cause your own revolution, so as always, getting Multiculturalism is a priority. Although, getting a strong revolution and switching sides to reset your infamy may help.
Ultimately, the big challenge is getting those couple big RNG moments right and then just destroying the US as soon and fast as possible. Eating the US is a huge amount of infamy and you have to spend roughly a third of the game just to become independent, so getting as much conquering time as possible and using as little infamy as possible is key.