Play and win the "Rise of the Mongol" scenario, This scenario is very much the same as the one in Civilization III. You start up in the northeast and shall fight down enough of the existing civilization south and west of you.
Tips:
When you start your game you have enough culture to by two social policies, don't wait for the second turn to remind you. That way you can complete and use the benefit at once. ie upgrade units cheaper and get 50% more XP and gold from slayed enemies.
Do not upgrade all your horsemen to Keshik because they are ranged and can't capture cities. You need to keep at least one regular horseman around for that. Or you will have to drag around a slower unit with your army for this purpose.
City-states do not have any civilization protecting them Turn 1 so you can encounter them and start a War first turn you won't have to deal with any allies. The AI will form these during their first turn which are after you. So Take this opportunity to take out the city State south of you quickly.
Do not annex every city you come across, consider burning some down to make the one left grow better.
This scenario is running on vanilla Civilization settings while
The khan citadel improvement do not grant any culture border if your used the expansion rules so you probably never use them in this scenario
And pillage enemy improvements only grants gold not health independent what the text claims
And give you a opportunity to play for completing the social policy "freedom, autocracy and Order" trees that are gone if you got the expansion DLC installed and you don't have the habit to disable them.
The scenario description is kind of vague but you should spend some round taking out city-state even if they aren't required to win. Civil-States can be annex without need for unhappiness ie Courthouse and all that on top of that you get a reward depending on type of city state. Military gives 2-3 new units in your capital so a good way to enlarge your army. Culture gives a free Social policy, Trade seem to give 500 gold. These should be seen as support town building your army and on the higher difficulties happiness.
You need to defeat four of these: (within 100 turns?) That gives you 25 turn each but I did it easily after understanding the rules concepts above on a fresh restart. Got more then 25 turns to spare on Settler and I did certainly not optimize my approach I still learned how the map looked like.
Western China with their City-State ally Korea a short distance South west of the start.
Western Xia and their potential ally China South of you, if you didn't start that war turn one. The two Chinese civilization will jump in and fight each other when you start a war with either one so making your first war easier while the other often will grow in strength and size.
Japan is located on the island to south east but you will need to research technology and fight a battle from the sea, I suggest you leave them alone out there.
West following the roads in the Desert are two City States Uighur (yours for the taking early in the game)
and Almaty and their ally Persia. This is a civilization that you basically must defeat to reach most other efficiently
You can reach India through the mountain just before reaching Persia or by going through one of the three city states forming a wall Lhasa, Dali and Dai Vet. South of the china block. But if you intend to go for them you can simply keep following the road in Persia. When I played I just threaten them enough to supply me with their gold and luxery and moved on to other targets.
West of persia is another wall of two city states Georgia and Abbasids behind this wall are the Arabs civilization together with Crusader states located.
North west corner of the map above Persia is the Russian civilization and a City state of Hungary
and all the furthest to the west behind Arabs or below Russia is the Byzantium Civilization which you most likely never need to fight unless you play on the higher difficulties which claim to require more defeated civilizations.