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