Image: UbisoftOfficial screenshot from Ubisoft.
A Modern Babylon is the story achievement for completing Memory Sequence 3 of Assassin's Creed Syndicate. It comes at the end of Sequence 3, where the twins settle into London, meet Abberline and start taking Whitechapel back from the Blighters.
Play the main memories of Sequence 3 through to the end. Optional objectives do not matter for this one; only the 100% sync achievement, Mentor, asks for those.