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