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