at least 7 to 9 stars and 300 to 800 planets
And how many weeks does it take to play a map of that size? Seriously, I get exhausted on a 100-planet map, which is why my typical game is done on the 69-planet map I mentioned. (I've reached the point where I almost never play any other maps in offline games. Large enough to make rushing not viable, small enough to still be playable.)
Anyway, do the math. 12 artifacts, at 15% chance, would mean that you'd need 80 colonizable planets just to have an average of twelve artifacts across your empire, and you'd have quite a bit of duplication. (That's assuming it's 15% per planet, not 15% per exploration, but the rarity I see in a typical game seems to bear that out.) By the end of a game you'll control every planet, although home planets never have artifacts. So, as long as you play on a map that has ~150 planets or more, you'll have all the artifacts you need.
Of course, if all you want is the achievement, there's nothing to stop you from making a custom map and setting the artifact density to 100%. Even a fairly small (20-30 planet) map would probably have all twelve in that case. I'm not sure what'd happen if you set it higher than 1.0; could you have multiple artifacts per planet? (Probably not.)
