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