Try building The Sistine Chapel and run a State Religion.
Try building your state religion buildings as soon as possible. 1000 years after building a structure, its culture gets doubled and this includes any bonuses like the one from The Sistine Chapel. That's 26 culture/turn from just a Temple and Monastery, which you can build anywhere as long as you have the techs.
A 1000 year old Cathedral also adds 10 culture/turn on top of the +50% bonus. A 1000 year old Holy Shrine even adds 18 culture/turn, before any multipliers.
Talking about multipliers, be sure to run Free Speech as soon as possible (+100%), focus building Cathedrals in your three main culture cities (+50%/Cathedral), build Broadcast Towers whenever they're available (+50%) and perhaps take a shot at Broadway, Hollywood and Rock and Roll if it's late in the game (+50% each). There is also the Hermitage national wonder (+100%). Getting +250% culture in your main cities isn't that hard.
Then there's corporations like Sid's Sushi Co., Creative Constructions and Civilized Jewelers adding culture per resource in your posession. Trade for more instances of these resources to maximize the cultural output of these corporations. The other bonuses (food and production) from these corporations also help you achieve your victory (more specialists and more buildings).
And of course, specialists, the culture slider and production converted to culture, etc.
