At every continent
The player’s country:
- owns a province in Europe
- owns a province in Asia
- owns a province in Africa
- owns a province in North America
- owns a province in South America
- owns a province in Oceania
To unlock this achievement, the player must own one province on each of the 6 continents in game.
The fastest way to get this achievements (as any country) is to unlock Exploration ideas as the first idea group, to be able to explore, but also for the casus belli it gives against primitives. Expansion ideas is also very useful for the CB it gives against African and Asian countries. If the player is looking for a peaceful way to obtain this achievement, note that European provinces are almost fully occupied; only the other 5 continents offer chances for colonization.
Since Portugal has its own idea that extends colonial range by 25%, and it already has foothold in Africa, it is considered the best choice for this achievement. All the player has to do is maintain good relations with Castile or Spain. The player may occasionally declare war on Morocco to avoid worry about defending Portugal's foothold in Africa. If the player maintained good relations with Castile (preferably allied), a war against Morocco should be relatively easy. Portugal's holdings in the Azores and Madeira make it easy for the player to get early colonies in the Caribbean (North America) and Brazil in (South America). Colonial nations do not count towards the achievement but unfinished colonies do. Colonial nations form when the colonizer has five colonies in one colonial region. Portugal also has the potential of being the first to be able to colonize South Africa which is crucial for reaching Oceania and India. When the player discovers the province of "Goa" there is an event giving you the province. This will probably be the players first Asian province, and their foothold for reaching Oceania.
Castile is also an interesting choice due to their colonization potential. However unlike Portugal, they don't have a colonial range bonus nor do they have lands in Africa. However their missions and strong armies ensure they can already take on Morocco. Because South Africa is crucial to reach SE Asia and Oceania, getting there as soon as possible is recommended. Since the player only needs one province on each continent, simply colonize one province in northeast Brazil and Trinidad, the island just north of Columbia. With the colony in Brazil the player should be able to colonize a South African province. After the colony self-sustains, the player can choose to invade the Maldives and/or colonize any of the Indian Ocean islands depending on colonial range. With one of these Asian islands the player should be able to access Australia. Another option is to colonize a province in Central America, and then go around the Pacific Ocean colonizing provinces in Alaska and Eastern Siberia, eventually reaching the Philippines and Western New Guinea (strangely, only the western half of New Guinea counts as part of Australia, while the eastern half is considered Asia).
Ottomans is also an interesting choice. They may only be in Europe at start but with their militaristic national ideas, they have the potential to expand into Asia, and with their unique missions will usually want to conquer Egypt (which is in Africa) from the Mamluks. This gives them access to the Red Sea allowing them to reach Oceania without colonizing South Africa. Colonizing in South Africa is recommended however, to gain the colonial range needed to reach America. The only difficulty is reaching North America, due to lack of range and the proximity of the other colonizers in North America.
Castile and Portugal are a lot closer to the Americas than the Ottomans, giving the Ottomans a disadvantage in the Americas. The player may want some land in Italy to extend colonial range westwards, and the easiest to reach is Naples, initially in personal union with Aragon. Much of the time, Aragon will fall in a personal union with Castile via a special event, if this happens, Naples will be in personal union with Castile and with their usually strong navy will be hard to conquer. To avoid this, the player will want to attack Naples as soon as possible.
If the player is lucky, Castile will take over Aragon's mainland instead of gaining a personal union. If that happens, it's very likely they were forced to release Sardinia. In this case, conquer Sardinia to further extend colonial range. Don't attempt this with Corsica, unless Italy has left the HRE or the player is confident about taking on the Holy Roman Emperor and their allies. If no great power allied Aragon when Castile destroyed their mainland, attack Aragon and take all island provinces (full annex if they only have island provinces left).
This should give the player enough colonial range to reach the Americas. If it doesn't, just keep leveling up diplomatic technology. The player may want to invade Qara Qoyunlu to get access to the Persian Gulf which helps get to Oceania faster. If this still isn't enough, invade the Timurids (once Ottomans own Egypt) and take coastal provinces (the Caspian Sea doesn't count). The player may even want to go further and invade India to extend their colonial range. Once the player reaches Oceania and sends a colonist to one of its provinces, the player won't have to worry about this. When the Ottomans have teched up enough to reach America, their best choice for colonization is probably Trinidad, which is rarely colonized due to its high native aggressiveness. South America is usually sparsely colonized (even the northern part). Colonize that part of South America and unlock this achievement.
Russia is a very specific colonizer, since they colonize not to the West, but to the East. However, the Earth is round, so the result is ultimately the same.
The player will naturally colonize the Siberia, the player doesn't even need exploration ideas to do it since Siberian Frontier idea automatically discovers all provinces adjacent to Russia. Once the player reaches Okhotsk, build some ships there and send them out on exportation missions. This way you can arrive to Philippines (and, ultimately, Western New Guinea) and Pacific North America.
That covers Europe, Asia, Oceania and North America. To get to Africa, colonise any island in the Indian Ocean if the players colonial range isn't enough. If the player is lucky, the Cape of Good Hope will be free. Madagascar will be enough for the achievement, but the cape has more valuable provinces than Madagascar.
That leaves only South America. By the time the player has a foothold in Alaska/California, there will probably be very few uncolonized or native coastal provinces left. If there are none, the player must resort to warfare to gain the needed province.