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