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