A1
: 
Set it on beta scenario and just build one city and win with either economic or culture. do not flip citys to yours and settle the first settler after 100 gold in your city.
A2
: 
You can take over other cities by attacking just don't start any new ones using settlers. As well I'm not sure if flipping enemy cities affects this or not.
A3
: 
Just play as the Mongols. You will capture cities as you invade barbarian encampments, but these do not count against you. When you get the free settlers at 100 gold, just have them join the city instead of founding a new one. This is one easy achievement.
A4
: 
You don't need to worry about flipping cities. You will receive the achievement as long as you only BUILD one city. You can flip all within range and still get it.
A5
: 
Play as the Mongolians and attack the Barbarians. Conquered Barbarian camps become Mongolian cities but don't count against the city count for this achievement.
A6
: 
Play as the mongols and take over barbarian villages. These do not count. Don't settle any cities, just conquer and you will get this victory.
A7
: 
The absolute easiest way to win is Mongols on the Beta Centauri scenario - in fact, you can do this pretty easily on Deity level and knock out a number of achievements. When I did this I got a map with a huge continent and in a matter of about 15 minutes, got 20 cities where the other civs had 2 or 3 tops.
You can win all but the Tech Diety achievement this way by building up your cities until you get to either the cultural or banking win scenario - start building the wonder, and make sure you save a turn or two before it's done. After winning, load that save and change the wonder to something else (ideally the other winning condition) and save again right before winning, then reload and complete the conquest victory.
A8
: 
I won this on my first try all I did was take out a ton of barbarian cities giving my guys infantry upgrades, maxed them out off barbarians then made 2 armies like this and had them play D never got attacked once and won a economic victory this was on king difficulty
A9
: 
Just hunker down, load up on defenses then go for culture, by the time the cities even found me I was nearly ready to win by economic or cultural, and this was on diety
A10
: 
Build up your cities and when you are close to winning pull out all of your armys and place them in one city.. the others will be taken over.. you will be left with one city
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