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