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