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