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