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