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 Ending 1 of 4
Steal 2000 coins after the Golden Rule is broken
Trigger The Golden Rule by stealing 5 times
Dodge 3 boulders
Use Photo Mode
Reach Ending 2 of 4
Enter the upper cistern in an unconventional way
Find treasure using the golden bow
Survive the Palace
Discover Underworld icons Sisyphus, Tantalus, Ixion and the Belide
Save Ulpius's life
Get rejected by Aurelia
Skip the city tour
Gild your first thing
Learn the true identity of the stranger by the river
Save Fabia's life
Solve Vergil's problem
Save Iulia's life
Loop through time once
Read 10 different grafitti
Enter a villa with a daring leap
Pick up the sponge on a stick
Discover what lies beneath the city
Reach Ending 3 of 4
Reach Ending 4 of 4
Free the captive and shoot her captor with your gun
Loop through time ten times
Confront the creator of The Golden Rule
Find all three missing persons
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
Die from hornet stings
Assemble as many people as possible in the Museum
Allow Fabia to die in the collapsing temple
Lie 10 times
Have Duli released from his cell
Help Galerius romance Equitia