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