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