The player’s country owns and cores the provinces of:
The achievement is relatively simple to get. The player has to conquer three likely non-western provinces as a western power which should be easy given the technological disparity to between the west and the rest, especially in the late game.
Expansion ideas will give an automatic CB against Asian tech nations and this will allow for easy expansion by European powers into the Indian Ocean region. The expansion CB does not apply to Muslim nations. Religious ideas can also be helpful as the Deus Vult idea gives a free CB against nations of different religious and allows for faster conversion of heathen lands.
The Expansion CB should allow for an easy conquest against Malacca. Wait until the AI is busy in a costly war, then strike with combined land and naval forces. Remember Western troops will be far superior and the player only needs one province so the war should be quite easy.
Expansion into the gold mines of East Africa will provide an economic boost and will allow for further conquests up the coast and into the Gulf of Aden region. If possible, attacking an ally of whoever owns Aden can work but if this is not an option, simply taking a province that borders the same sea tile will allow for claim fabrication and a conquest CB. Usually Aden will not be in the hands of any major land power and while the Ottomans do tend to expand in that direction in the late game, if the player is fast, there should be no trouble in beating up Yemen or Oman for a single center of trade.
Hormoz has the potential to be more difficult as it could be owned by a large land power like Persia, but since the province needed for the achievement is an island, naval superiority will allow for easy occupation and then the player can use strategic allies in the region or their own armies to quickly finish off the war.