There are 12 Trophies that can be collected.

Bronze

Initiated
Complete the Initiation mission.

Thanks for Playing!
Finish one match of Gotham City Impostors.

Customizer
Unlock any locked loadout or costume item.

Total Victory
Win each game mode in Ace Chemical, Amusement Mile, Crime Alley, Gotham Power and The Docks.

Silver

Slap Happy
Kill 50 enemy players using the panic-slap melee attack.

Prestigious
Accept your first Promotion.

Gearhead
Complete all feats related to a particular gadget or support item.

Shower of Gold
Earn 50 gold medals in Challenge mode.

Kill Crazy
Earn a 10-kill streak.

Nemesaurus
Become a Nemesis 50 times.

Weapon Specialist
Complete all feats related to a particular weapon.

Hero of the Hour
Turn the tables in Fumigation when the enemy team's victory is imminent.

http://www.ps3trophies.com/forums/playstation-trophy-news/11431-gotham-city-impostors-trophy-list.html