Here is the full list of all 89 Egypt: Old Kingdom achievements.
Finish the second trial by subjugating regions one by one
Gather enough strength to complete the last trial
Finish the game with a score of at least 7 points
Finish the game with a score of at least 10 points
Finish the game with a score of at least 13 points
Finish the game with a score of at least 17 points
Finish the game with a score of at least 21 points
Finish the game with a score of at least 25 points
Finish the game with a score of at least 28 points
Finish the game with a score of at least 30 points
Finish the game with a maximum score
Complete the game with Ptah as your patron god
Complete the game with Horus as your patron god
Complete the game with Seth as your patron god
Finish the first trial by reducing the power of suspicion to 0
Finish the first trial by subjugating the keepers of the ancient traditions
Finish the first trial after choosing 'Hell on earth' prologue without recruiting workers
Finish the second trial by making all the regions surrender
Finish the second trial in 2 turns
Finish the third trial by defeating Narmer in a decisive battle
Finish the third trial by ambushing Narmer
Finish the third trial by ambushing Narmer without bribes or fortifications
Finish the fourth trial in any way
Finish the fourth trial only using sacrifices
Finish the fourth trial in 1 turn
Prevent the fifth trial by curbing the growth of separatism
Finish the fifth trial in any way
Finish the fifth trial only using combat
Finish the fifth trial with no combat
Finish the sixth trial in any way
Finish the sixth trial with no reforms or oppression
Finish the sixth trial in 10 turns or less
Finish the seventh trial in any way
Finish the seventh trial without help from the patron god
Finish the seventh trial in 1 turn
Finish the eighth trial in any way
Finish the eighth trial without help from the patron god
Finish the eighth trial by performing a miracle
Finish 'New settlement' quest without recruiting workers
Finish 'Assimilation of neighbors' quest before turn 50 without subjugation or patronizing
Finish 'Ascension of the tribe' quest by building a temple in 3 turns
Finish 'Creation of the chiefdom' quest without annexation
Finish 'Creation of the chiefdom' quest before Narmer attacks
Finish 'Relocation of the capital' quest by finishing the construction of a palace and a temple at the same time
Finish 'Stone of Memphis' quest before turn 115
Finish 'The Copper of the Sinai' quest before the start of the fifth trial
Finish 'Conquest of Lower Nubia' quest peacefully
Finish 'Conquest of Lower Nubia' quest within 5 turn from the end of 'The Copper of the Sinai' quest
Finish 'Conquering the kingdom of Seth' quest before turn 230 with Horus as a patron god
Give no correct answers on a quiz
Give 5 out of 10 correct answers on a quiz
Give 10 out of 10 correct answers on a quiz
Build a pyramid during the second dynasty
Finish constructing the project of Khasekhemwy during the second dynasty
Sacrifice 4 workers while constructing a single tomb
Build a temple on every hill in Memphis
Finish constructing a pyramid with all settings maxed
Finish constructing a pyramid with all settings on the minimum
Make all fourth dynasty tombs colossal and out of red granite
Finish the game without losing a single battle
Finish the game without killing animals
Have lions, crocodiles, hippos, hyenas, antelopes, aurochs, wildfowl and fish tamed in Memphis at the end of the game
Perform 20 successful hunts in a single playthrough
Finish the game without having more than 50 workers
Finish the game with a worker limit at 100
Finish the game without help from the patron god
Finish the game without worshipping gods even once
Finish the game without constructing graveyards, tombs or pyramids
Discover 'Step Pyramids' technology before Imhotep is born
Discover all technologies in the game
Complete 'Bandit network' event on the next turn after it appears
Find the RIver God in the Nile and start worshipping him
Rob a caravan with Seth as a patron god
Arrange a marriage between Horus and a wealthy princess
Enter a war against a tribe living outside Nile valley and make it surrender
Prevent a flood by reducing its chance to 0
Stop an epidemic that engulfed 3 or more areas, before it stops naturally
During a 'Royal festival' event, outrun a bull while the success chance is 50% or lower
Raise your relations with the Bull tribe to 100
Annex Lebanon
Explore entire map of Egypt
Discover Germany during travels
Have more than 10 tribes subjugated at once on the Egypt map
Reach luxury growth of 50 using trade
Send an expedition for incense
Complete expeditions to 10 different location on the Egypt map in a single playthrough
Tame a carnivore
Domesticate 3 animal species in a single area
Win a battle with a balance of power of 35% or less