For this achievement you will need to build all wonders in the base game. Wonders added by Gods and Kings and Brave New World are not needed for this achievement. Here is the list of all the wonders (by era) you will need and their prerequisites (prerequisites are from BNW). World wonders (of which only one can exist in the world) are marked (W) and National wonders are marked (N).
Ancient Era
Great Library (W): Requires Writing technology.
Stonehenge (W): Requires Calendar technology.
The Pyramids (W): Requires Masonry technology and Liberty policy tree unlocked.
Classical Era
Colossus (W): Requires Iron Working technology. Can only be built in coastal cities.
Great Lighthouse (W): Requires Optics technology. Can only be built in coastal cities.
Great Wall (W): Requires Engineering technology.
Hanging Gardens (W): Requires Mathematics technology and Tradition policy tree unlocked.
Heroic Epic (N): Requires Iron Working technology and Barracks built in all cities.
National College (N): Requires Philosophy technology and Library built in all cities.
National Epic (N): Requires Drama & Poetry technology and Monument built in all cities.
Oracle (W): Requires Philosophy technology.
Medieval Era
Angkor Wat (W): Requires Education technology.
Chichen Itza (W): Requires Civil Service technology.
Hagia Sophia (W): Requires Theology technology.
Ironworks (N): Requires Machinery technology and Workshop built in all cities.
Machu Picchu (W): Requires Guilds technology. City must be within 2 tiles of a Mountain.
Notre Dame (W): Requires Physics technology.
Oxford University (N): Requires Education technology and University built in all cities.
Renaissance Era
Forbidden Palace (W): Requires Banking technology and Patronage policy tree unlocked.
Hermatige (N): Requires Architecture technology and Opera House built in all cities.
Himeji Castle (W): Requires Gunpowder technology.
Porcelain Tower (W): Requires Architecture technology and Rationalism policy tree unlocked.
Sistine Chapel (W): Requires Acoustics technology.
Taj Mahal (W): Requires Architecture technology.
Industrial Era
Big Ben (W): Requires Industrialization technology and Commerce policy tree unlocked.
Brandenburg Gate (W): Requires Military Science technology.
Louvre (W): Requires Archaeology technology and Exploration policy tree unlocked.
Modern Era
Cristo Redentor (W): Requires Plastics technology.
Eiffel Tower (W): Requires Radio technology.
Kremlin (W): Requires Railroad technology and Order ideology adopted.
Statue of Liberty (W): Requires Replaceable Parts technology and Freedom ideology adopted.
Atomic Era
Pentagon (W): Requires Combined Arms technology.
Sydney Opera House (W): Requires Ecology technology. Can only be built in coastal cities.
Information Era
United Nations (W): Requires Globalization technology. Only exists pre-Brave New World and doesn't seem to be required anymore as I never built it and still got the achievement.
As you can see, you will need at least two playthroughs to get all of the wonders (assuming the AI never beats you to one) as adopters of Freedom will not get access to the Kremlin and adopters of Order will not get access to the Statue of Liberty (an Autocracy adopters get neither!) unless you build one and then switch ideologies.
If you're not sure what wonders you still need for the achievement (or any others) you can check by enabling the achievements_debug log. To do this go to My Documents/My Games/Sid Meier's Civilization 5 and open config.ini with your preferred text editor. Find the line that says LoggingEnabled = 0 and change the 0 to 1. Now the next time you start the game a file called achievements_debug.txt will be created in the logs folder. Open the file and scroll down towards the end. The wonders you need will be between the lines DBG: Steam Stat: ESTEAMSTAT_ANGKORWAT = # and DBG: Steam Stat: ESTEAMSTAT_OXFORDUNIVERSITY = #