True Rogue Mode has been added by the new DLC.
To start it you have to slect a new EMPTY save slot and then select Play Special modes and then True Rogue Mode.
This mode has you completing biomes in ramdom order and to get this achievement you need to finish the run with a single heir, so if you die, erase that save slot and start another.
This might sound daunting, but if you use House Rules, and toggle down all damage and other accessibility options this will be much much easier.