Alright, I have organized the Brave New World achievements into categories now. This is what I know so far:
Leader Achievements:
In Hoc Signo Vinces - Beat the game on any difficulty as Maria I.
King of the Wisent- Beat the game on any difficulty as Casimir.
Pedro's Party People - Beat the game on any difficulty as Pedro II.
Tablet Tech Pioneer - Beat the game on any difficulty as Ashurbanipal
Wanna Be the King of the Zulus - Beat the game on any difficulty as Shaka.
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Ideology Victory Achievements
Axis Powered - Win a Diplomatic Victory using the Autocracy Ideology.
Better Red Than Dead - Win a Conquest Victory using the Order Ideology.
Everybody Wants to Rule the World - Win a Conquest Victory using the Autocracy Ideology.
Games Without Frontiers - Win a Diplomatic Victory using the Freedom Ideology.
One Small Step - Win a Space Victory using the Freedom Ideology.
Rocking in the Free World - Win a Cultural Victory using the Freedom Ideology.
Strength Through Joy - Win a Cultural Victory using the Autocracy Ideology.
Workers of the World - Unite! - Win a Cultural Victory using the Order Ideology.
Yuri-ka! - Win a Space Victory using the Order Ideology.
Civilization-Specific Achievements:
British Invasion - Perform a Concert Tour with a British Great Musician in American territory.
Knowledge is Power - As Assyria, use a Royal Library filled with a Great Work to train a unit that begins with a promotion.
Poland Can into Space - As Poland, win a Space Victory.
Pyramid Scheme - Playing as France, get the Louvre to the maximum theming bonus of 16.
Raiders of the Lost Ark - Have your American Archaeologist extract an Artifact from Egypt with a German Archaeologist within 2 tiles.
Run 50 Miles and Fight a Battle - As Zulu, have an Impi earn all of the special promotions.
Vote for Pedro - As Brazil, win a Diplomatic Victory.
What's Yours is Mine - As Portugal, construct a Feitoria in a City-State that is allied to another civilization.
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General Achievements:
Built in (Almost) a Day - Complete a Wonder in a city with three Trade Routes supplying production to it.
Greed is Good - Have a city with the Colossus, Petra, a Caravansary, and a Harbor.
Highway Robbery - Plunder a Caravan Trade Route.
It Belongs in a Museum - Have Artifacts from 10 different City-States in the Museums and Wonders in your civilization.
Losing My Marbles - Extract 5 Artifacts from the territory of another major civilization.
Merchant Prince - Generate 200 gold per turn via Trade Routes.
Radio Free Europe - Adopt the Freedom Ideology and fill 10 Broadcast Towers with Great Works.
Silk Road - Connect to the Arabs, China, India, the Mongols, and Persia at the same time using Caravans.
Soma Tablets for Everyone - Reach a Happiness level of over 100 for your civ.
Tear Down this Wall! - Force an AI player with the Order Ideology to switch to Freedom.
That's XCOM baby! - Have your XCOM Squad go from 100 health to 0 in a single AI turn.
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World Congress Achievements:
Dark Horse - Win a Diplomatic Victory without ever being the host of the World Congress.
Flip-Flop - Propose to repeal an active Resolution which you had originally proposed to enact.
Herculean Effort - Complete all International Projects in a single game as the highest contributor.
Lingua Franca - Found the World Congress and remain its host for the entire game.
Policy Achievements:
Artistic License - Fully explore the Aesthetics Policy track.
Legends of the Hidden Temple - Fully explore the Exploration Policy track.
Scenario: Scramble for Africa
Discoverer - Playing as Italy in Scramble for Africa, earn the VP for finding two Natural Wonders.
Dr Livingstone I presume? - Playing as Belgium, move your Stanley Explorer to within a tile of Englands Livingstone Explorer.
I Prefer my Africa Scrambled - Win the Scramble for Africa scenario as any civ on any difficulty.
Nigerian Bank Account - In Scramble for Africa, marry Sokoto or Bornu.
Ottoman Carpentry - Win the Scramble for Africa playing as the Ottomans on Deity.
Praise the Victories - Win the Scramble for Africa playing as the Boers on Deity.
The Rhodes Colossus - Playing as England in Scramble for Africa, complete a railroad from Cairo to Capetown.
Scenario: The American Civil War
Glory, glory, hallelujah! - Win the Civil War scenario playing as the Union.
Pickett's Recharge - Capture Gettysburg with a Confederate Infantry unit possessing the George Pickett promotion.
Red Badge of Courage - Win the Civil War scenario on Deity.
Sheridan's Valley Campaign - As Union, control Winchester, Front Royal, Harrisonburg, Staunton, and Lynchburg.
Standing like a Stone Wall - Win the Civil War scenario playing as the Confederates.
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Culture references (this is just off the top of my head):
Better Red Than Dead - A play on the "Better dead than red" anti-communism slogan.
British Invasion - A musical movement in the early and mid-60's, most famous for The Beatles.
Built In (Almost) A Day- Probably a take on the phrase Rome wasn't built in a day.
Everybody Wants To Rule The World - a song by Tears for Fears.
Flip-Flop - A political term for someone changing their position for political gain.
Games Without Frontiers - a song by Peter Gabriel.
Greed Is Good - A quote from Wall Street.
It Belongs In A Museum - A line said several times in the beginning of Indiana Jones and The Last Crusade.
One Small Step - Some of the words Neil Armstrong spoke when first walking on the moon.
Raiders of The Lost Ark - The first Indiana Jones movie.
Rocking In The Free World - A song by Neil Young.
Tear Down This Wall! - A historic quote spoken by Ronald Reagan about the Berlin Wall.
Vote For Pedro - A phrase associated with Napoleon Dynamite.