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