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Enforcers are the biggest and toughest of the henchmen.The enforcer in the picture works for The Penguin. Black Mask has a lot enforcers just like The Penguin.

Incident Reports

Before Arkham Origins Incident

Arkham Origins Incident

While Batman was tracking the Penguin, an Enforcer attempted to waylay him, though he was taken out easily. Later, in the Sionis Steel Mill, an Armored Enforcer was dispatched to keep Batman from rescuing Black Mask, who was being held captive by his former men. Enforcers were then encountered two more times in the Gotham Royal Hotel, and two more times at Blackgate Prison.

Various unaligned enforcers could be encountered in crimes in progresses. 

Cold Cold Heart Incident

At GothCorp, Penguin's Enforcer named Fitzy arrived with the other Penguin thugs to take down Batman and he got taken out.

Between Arkham Origins, Arkham Asylum and Arkham City Incident

Arkham Knight Incident

Known Enforcers in Gang Groups