American Indians: Colonize America as any Indian nation. If it needs to be more difficult, make it require colonizing the entire 13 Colonies area, or establishing the colony in an area of the Americas that has not yet been discovered by anyone in the Western or Eastern tech group so that the Europeans can "discover" Indians in the Americas.
West European Trade Company: As an Indian state, establish a trade route that ends in you collecting in any European trade node. Additionally, you must have at least 51% trade power in this node.
Colonies? We Don't Need no Stinkin' Colonies!: As any historical major colonial power (Castille/Spain, Portugal, France, or England/GB), hold no "distant overseas" provinces at any point from 1444 to 1821.
Extra-Alternate History: Load an exported Crusader Kings II game.
Violence is not the Answer: As any nation, gain at least 30 provinces without ever taking any provinces (for yourself or for any vassals) in a war. Renovatio Imperii doesn't count. Also, there may be some restrictions, such as Denmark cannot do it due to starting with Sweden and Norway in a PU and Holstein as a vassal.