Note: The description is misleading as you only have to complete the campaigns of The Age of Kings, not the campaigns of The Conquerors.
There are 5 campaigns in The Age of Kings:
1: William Wallace: Learning CampaignThe William Wallace Campaign Completed achievement in Age of Empires II (2013) worth 18 points“We come here with no peaceful intent, but ready for battle, determined to avenge our wrongs and set our country free. Let your masters come and attack us: we are ready to meet them beard to beard.” - (1297) William Wallace 2: Joan of Arc3: SaladinThe Saladin Campaign Completed achievement in Age of Empires II (2013) worth 35 pointsBy studying the campaigns of Salah al Din Yusuf ibn Ayyub, or 'Saladin' as he was known to the crusaders, you can know that there are many aspects to the great heroes of the Middle Ages. The lessons of his campaigns will guide you in your other conquests. 4: Genghis KhanThe Genghis Khan Campaign Completed achievement in Age of Empires II (2013) worth 37 pointsHis enemies know only the ruthlessness and speed of the great Khan’s conquests - but the greatest generals also know the tools of cooperation, alliance, and loyalty - these will serve you well in future campaigns. 5: BarbarossaWin every scenario of each campaign using the cheat code “i r winner”. Then, to trigger the achievement, win any scenario of any campaign without using cheat codes. The quickest scenario is the 1
st scenario of the William Wallace Learning Campaign: Marching and Fighting.