Here is the full list of all 9 A Night in the Forum trophies - there are 1 bronze, 7 silver and 1 gold.
Organise the wax tablets in the Eastern Archive
Inspect the Temple of Mars and lock its door
Clean the ashes near the altar in the Main Square
Light the fires inside the Hall of the Colossus
Rearrange the furniture in the Urban Tribunal
Search for Senator’s pallium in the Eastern Tribunal
Check work in scaffolded area and collect any tools left behind
Collect any items left in the Main Square
Complete all your tasks and return to the modern day