El Dorado no estado
Starting as Mutapa, conquer Sofala and make sure Kilwa has no gold income before 1455.
Based on the EU4 masters tournament and the Kilwa challenge where you have to have as much gold income as possible within 30 minutes(real time). Some people did really well and others... lost to Mutapa and one even had no gold income at the end of the challenge.
Prussian Space Marines
As Prussia, have military tech 32, 100% army professionalism, and 100 army tradition while having at least 100 regiments and 15 or less provinces.
There can only be one
Starting as Ulm, own Okinawa under direct control or the possession of a non-tributary subject while Ryukyu either does not exist or is a subject of Ulm.
Okinawa is the capital and sole province of Ryukyu at the start of the game. Ryukyu and Ulm are both OPMs at the game start in bad positions that have risen to memehood. Ryukyu has an achievement for owning the world, while Ulm does not have any achievements(that are unique to Ulm), so Ulm should have some achievement involving the destruction of Ryukyu.
The great escape
Starting as Brittany, move your capital to the new world and own the entire new world directly while holding no land in the old world.
The journey of a thousand miles
Starting as Chukchi, conquer Lisbon.
This are the two owned provinces that are about as far as possible at game start, and while there are farther provinces from Chukchi at the start in Africa, Lisbon would be much harder to take than one of those. The name for the achievement is from the quote, "A journey of a thousand miles begins with a single step".