Batman stood in front of a billboard with a message written by the Riddler. You can only see the clues (which appeared as green text) by turning on detective mode (think of it like Samus’ scanning visor). Just like Batman: Arkham Asylum the Riddler hid trophies to collect throughout the city.
You can see blips on your radar where Riddler’s thugs are and Batman can beat them up for more information. However, you need to use some restraint and keep a goon with a ? mark over his head conscious. Batman can interrogate him (Batman Begins style) if he’s the last thug standing. This time the Riddler hid his trophies within traps that make use of Batman’s gadgets. While these are an optional objective, finding trophies is the way to catch the Riddler.
One other interesting bit about Batman: Arkaham City is I saw Jack Ryder in the game too as an ordinary newscaster. Batman rescued him from a mob as he scurried away from the fight.