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