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