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