The Bronze Trophies will be awarded for exploring various systems of the game, such as Researching, Modifying Weapons, Hacking, and Crafting.
The Silver Trophies are a bit more difficult to get and will require a significant amount of extra-work. The “Historian” Trophy for instance, is awarded for finding every single audio diary in the game.
The Gold Trophies are meant to reward a player’s second or third descent into Rapture. The only one unveiled so far is the one dubbed “Brass Balls”, reserved for those skilled enough to win BioShock on Hard difficulty with the Vita-Chambers turned off.
The Platinum Trophy (or Trophies) remains cloaked in mystery, with the announcement saying only this: “Its glistening mass is reserved for those few who can stare down a Big Daddy without shivering.”