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