You will find the child crying with his mother across from where the shooting gallery is. He'll say he lost his bear by the shooting gallery after he was yelled at. Head over there, and begin. You will need to complete all three rounds before the curator gives you the teddy bear. Use weapons that have a medium-sized clip, and decent range. Avoid using weapons like the Helsing, Tihar or Bolt-action rifle. Stick with the Bastard, Kalash, or the Revolver. You'll need to kill 5 rats in 40 seconds in the first round, 10 rats in 40 seconds in the second round, and 15 in 40 seconds in the third and final round. You'll receive a nice amount of gold, as well as the Teddy bear. Head back over to the kid, and hand it over for the achievement.