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