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