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