Kill 1 Needler.
You first come in contact with Needlers in the Grand Hotel, a short while into the game. Use your pistol and shoot them as they try and break into the elevator.
Some general fighting tips for needlers when you encounter them:
-Melee: It can get dangerous going melee with these guys as they are quick and can do some damage, but is the best way. Use the Axe, let them attack, dodge and then counter with X or A, then do an A,A combo, then dodge back and rinse and repeat.
-Pistol: Regardless of the tip the game gives you about shooting them in the head, its a hard thing to do and not really worth it. They will continually block the bullets with their arms and are only open right before an attack, which most likely will result in getting hit, so don't bother.