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