Very short guide to get the Rise of the Machines achievement.
How to Get the Achievement
Simply play any machine empire and set the number of AI empires, marauders, and fallen empires to 0 during game setup.
If there are no organic/lithoid empires in the galaxy you will automatically get this rare achievement on day 2 after you unpause the game. You don't even need to be a Determined Exterminator, any machine empire will do.
This method has been confirmed to work in version 2.5 of the game. I make no guarantee it will work in older or newer version of the game.