Catherine the Great is one of the best leaders in for a Cultural Victory due to her Star of the North ability, which boosts Culture from Great Works and allows her to advance Technology research alongside Cultural growth.
This will be a highlight of Catherine the Great's campaign strategy, as a Cultural Victory hinges on strong Production (especially during the Antiquity Age), as well as Science to ensure access to the best Food, Production, and Culture buildings.
To achieve the Cultural Victory, Catherine the Great's best options are Greece in Antiquity, Norman in Exploration, and Russia in the Modern Age. Each of these civilizations complements Catherine the Great's ability and will allow her to take full advantage of both Culture and Science yields during each Age.
The Cultural Victory in includes the Wonders of the Ancient World, Toshakhana, and Geographic Society Legacy Paths, which Catherine will have no trouble completing in a timely fashion.
With these civilizations, she will also be capable of developing a powerful defensive Army, and will have sufficient Influence to build alliances and become Suzerain of City-States.