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