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So if you want to get this quickly or can't win on Deity there's is an insanely easy way to unlock this achievement. Scroll all the way down for the short version.

From the main menu choose Single Player => Create Game => Advanced Setup.
Select the Deity difficulty.
Choose Peter (Russia) as you leader.
Scroll down and change Limit Turns to Custom and set Max Turns to 1.
On your turn build your city(ies), select any research, civic, production, select a government, Chiefdom's fastest, and/or fill your policy slots if you need to.
Once you end your turn the game will end and you'll have won.

You can also choose a starting era, map type, and map size that you haven't unlocked the achievement(s) for to easily unlock those as well.

This works because Peter starts with more territory than other leaders so you'll have a higher score. Note this is actually a Russian ability so if they release another Russian leader down the line it should work with them as well.

Hope this helps and thanks for reading.

TL;DR: Select Peter in a 1 turn game.