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