Here is the full list of all 36 Khan VS Kahn achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Demolish a building
Win with a military victory
Win with a science victory
Win by building the wonder
Build the final level of wonder
Build the fourth level of wonder
Build the third level of wonder
Build the second level of wonder
Build the first level of wonder
Win against all AI
Win a game with the orc race
Win a game with the elves race
Win against an hard AI
Upgrade a Shrine at maximum
Change the altar to pray the science god
Defeat the Necromancer
Build 2 houses in one game
Build 2 Taverns in one game
Change the altar to pray the gold god
Play against a friend
Win with a cultural victory
Build 3 farms in one game
Upgrade a house at maximum
Win against an easy AI
Win a game with the troll race
Change the altar to pray the wood god
Build a Shrine
Convert one man into soldier
Win a game with the human race
Win with a economic victory
Win against a medium AI
Build 3 Woodcutters in one game
A villager of yours die for nothing
Go hunt for the first time
Change the altar to pray the farm god
Upgrade the mine