The player’s country must have 200 cities to claim this achievement. Subject provinces do not count towards the necessary 200 provinces, this includes colonial nations. This achievement requires steady expansion throughout the game’s time frame. The big gameplay obstacles includes aggressive expansion penalties, overextension, and coring costs. Keep in mind that the province count is what matters, not the quality of the province. Hence, when negotiating after a war, it is better to demand several poorer provinces instead of one high value province. This achievement and the achievement Over a thousand can be done at the same time as doing the World Conqueror achievement.
An important way to minimize overextension and coring costs is using diplomatic annexation. Instead of directly claiming territories from a beaten nation in peace settlements, demand they become a vassal. This only works for sufficiently small nations (per base tax, not number of provinces). Otherwise, the peace settlement will cost over 100% which the game does not allow. Any vassal can be annexed by its owner. This not only gives every province directly to the owner, but automatically cores the provinces for the new owner at no cost to administrative points. The process should be much quicker as the annexation only takes as long as the vassal's total base tax in months. A nation must be a vassal for at least 10 years before it can be annexed, and the annexation process itself can takes time.
Once the nation is a vassal, check to see if the vassal has any core provinces held by other powers, and plan on get them back to the vassal before annexing them. A nation stays a vassal even if it grows bigger than the initial ceiling for being a vassal. Also, selling provinces to a vassal if they have a claim or a core on it and if its not yet cored it is a good tactic. After a minimum 10-year wait, the player is free to annex any vassal with a relationship of 190+ or more. Even if a vassal changes religion or government type and would be impossible to vassalize through diplomacy, the player can still annex any vassal using a diplomat.
Considering the role of diplomacy in pursuing this achievement, the diplomacy idea tree is a very good choice. It lets the nation have more diplomatic relationships which means more simultaneous vassals. Also, more diplomats to improve relations, fabricate claims, and actual annexation.
The Ottomans are a strong choice to pursue this achievement with. It has a national idea that reduces coring costs by 20%. Combine this bonus with the administrative idea adaptability (25% reduction) and having a diplomat create a claim on a province (10% reduction), the player will only pay 32% of the base cost in administrative points to core a conquered province. This means military expansion is a lot cheaper. Furthermore, the Ottomans have a lot of lower technology targets to the east and south-east, which means easier expansion.
Another strong choice is Qing (via Manchu, which in turn can be formed with any Jurchen culture country, although Jianzhou is the strongest choice to do this with), with its strong Banner regiments and the Manchu core cost reduction combined with the free cores on the entirety of China once you destroy Ming as well as gaining 3 free Marches thorough the mission tree which you can subsequently annex. The Qing are especially useful since the Unify China causus belli gives a 50% reduction to aggressive expansion and to annexation costs.
Another option is Russia (via Muscovy), due to the large number of Siberian provinces, easily conquered hordes, possible colonisation of the American West Coast and potential conquest of China. A fun one can be France by first doing achievement Big Blue Blob and then continue and take 100 provinces more.
For other game styles this can also be achieved by aggressively colonizing in the North Americas as the Aztecs and relieving the Inca and North American tribes of their lands. The player would do well to wall up the coastal provinces and than work their way inwards, take the Galapagos and Easter island to help prevent further colonization by the Europeans. Annexing the Inca will also give the player the achievement A Pile of Gold for owning 10 provinces of gold.
Finally, a player can play as a released colonial nation, such as the United States, and colonize the interior of the Americas. This can result in getting the Aggressive Expander achievement without aggressively expanding at all.