Batman/Joker said:
i really don't have a clue as to how they got them in there....but if you want to know why they're there, they're from past battles from Joker, Two-Face, etc....
Actually, aside for the giant Joker, which used to be a huge facemask of him instead of the card, all the other high profile souveniers/trophies aren't necessarily connected with the "big league" foes.
The dinosaur was a souvenier from the adventure "Dinosaur Island", an amusement park that used various giant animatronic dinosaurs as attractions (Batman #35, 1946).
The giant penny has nothing to do with Two-Face (who'd use a dollar, not a penny for choice) though in the DCAU, it's suggested that it IS from a Two-Face story, ("Almost Got 'im") but in the comics it is instead a memento of the "Penny Plunderer" case, (World's Finest #37, 1949), in which a villain based all his crimes around the concept of pennies.
Other commonly seen trophies include the bulletproof vest of the Rafferty Brothers and a selection of recognizable gimmick weapons, like some of Penguins umbrella's, and a pair of giant dice.
The Batman DCAU comic, came up with a simply magnificent idea as to the origin of the Hall of Trophies. We simply start with a scene from an early case, with a very young Dick Grayson as Robin standing on top of a downed robot T-Rex and begging "Can we keep him? Please? Huh? Huh?" to Batman. The idea being that the Trophies don't actually serve much of a function for Batman, but is more intended for Robin (As a sort of reward for having to forego his fondly remembered circus lifestyle, and constantly pretend to be not as bright, or fast, or strong, etc as he really is, in order to protect their identity). I just love that as a notion.