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