Here is the full list of all 40 The Forgotten City achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Reach Ending 3 of 4
Reach Ending 1 of 4
Finish the game without looping through time once
Reach Ending 2 of 4
Find all three missing persons
Reach Ending 4 of 4
Assemble as many people as possible in the Museum
Talk your way through every possible confrontation
Confront the creator of The Golden Rule
Have Duli released from his cell
Read 10 different grafitti
Loop through time ten times
Discover Underworld icons Sisyphus, Tantalus, Ixion and the Belide
Trigger The Golden Rule by stealing 5 times
Steal 2000 coins after the Golden Rule is broken
Dodge 3 boulders
Discover what lies beneath the city
Solve Vergil's problem
Save Ulpius's life
Find treasure using the golden bow
Get rejected by Aurelia
Learn the true identity of the stranger by the river
Survive the Palace
Use Photo Mode
Gild your first thing
Save Iulia's life
Enter a villa with a daring leap
Save Fabia's life
Loop through time once
Free the captive and shoot her captor with your gun
Enter the upper cistern in an unconventional way
Intimidate the creator of The Golden Rule
Reach the best ending with the smallest number of loops
Topple 10 peeled statues by kicking others into them
Pick up the sponge on a stick
Die from hornet stings
Skip the city tour
Allow Fabia to die in the collapsing temple
Lie 10 times
Help Galerius romance Equitia