Tiny

"Whatever I drop in that tank, just... vanishes. Poof. (laughs) Problem gone."

- Penguin to Batman about Tiny

Tiny was the giant great white shark that Penguin kept in his "Torture Chamber" in the Cyrus Pinkney's Institute for Natural History, and ate everything that entered the water tank.

Arkham City Incident
Tiny swam around in the tank of the former Terrors of the Deep exhibit at Cyrus Pinkney's Institute for Natural History, which had been repurposed into the Torture Chamber of Penguin's base. Tiny fed on anything that entered the tank's water. When Batman was hunting for Mr. Freeze within the Museum, the Penguin left three undercover cops on the frozen-over surface of the Torture Chamber to die of hypothermia and be eaten by Tiny.

Batman saved the undercover cops, and went on to rescue Mr. Freeze, and took a Disruptor from Freeze's Suit that disabled his Freeze Gun, which was being utilized by Penguin. On his way to the Iceberg Lounge, Tiny attacked Batman for getting too close, but Batman beat the shark down, and Tiny was never to be seen again after the encounter.

Arkham Knight Incident
Tiny is not seen in Arkham Knight, but a shark resembling him appears at the docks. During one of the random conversions Batman can eavesdrop on, one of Joker's former henchmen even asks his buddy (who is one of The Penguin's Henchmen) what happened to the shark (referring to Tiny).

GCPD Lockdown
Tiny is seen if Nightwing comes up to an aquarium with a plaque titled "Tiny" and will jump scare him.

Trivia

 * If Tiny killed you on the way to the Iceberg Lounge, the Game Over scene hint mentioned the Shark Spray from the 1966 Batman movie.
 * If you fell into the water after Penguin's defeat, Tiny will not eat you.
 * The Shark's corpse found in Arkham Knight is also possibly a reference to another dead Shark who can be found in Batman: Arkham City, at the northeast of Amusement Mile near Bane's Hideout. The Shark that appears in Arkham City is found hanging the same way Arkham Knight's Shark is.
 * The shark at the docks in the right side image is not far off the size of Tiny.
 * Tiny's skeleton is not detected by Detective Vision, due to the cartilage that forms it instead of bones.
 * The chances of the shark in Arkham Knight being Tiny are low as it confirmed he is alive in Nightwing's DLC
 * Despite being called Tiny, he is actually quite big.