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