Build any type of power plant, a Stadium (Modern Times required), then issue the "Host the Olympics" edict.

You cannot declare your independence. Do this early, while still a colony. Complete missions to earn mandate extensions until "Everlasting Colony" is earned.

Begin a sandbox game with unlimited money under the easy difficulty setting in the Modern Era. Build the maximum number of Science Labs, Colleges, and Observatories then fully staff them. Search for Inventors in your population by using the "Census" edict. You can also use your Spy Academy to steal technology from other superpowers, but this may not be reliable. Build Power Plants to provide enough power to the Science Lab.

Construct five Embassies and invite all foreign powers to each one. Note: This can be paired with the "For Science!" achievement or trophy.
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Faction leaders can be found through the game menu or by browsing your city. They will have a blue square above their heads. Select "Bribe". The amount of money required will depend on how much influence the leader has and the weight of the faction.