You will find the Berserker in 'China Town', the final chapter of Act 1. Lead her through the house by standing in the doorway you want her to go through, shooting her, then jumping out of the way right before she hits you. Repeat until you lead her outside, then use the Hammer of Dawn on her. Hit her with it twice to obtain the achievement.
There is also another berserker near the beginning of Chapter 2 of Act 5. Just lead her off the end of the train in the same fashion as described above.
This achievement can be done on Co-Op. If done in Co-op, it will not matter who actually kills her. The achievement will unlock for both players, assuming neither one already has it.
The Berserker must be killed on Hardcore difficulty to count. Not Casual or Insane.
Berserkers are blind. They will not respond to your sight, but rather the noises you make or contact you make with her.
You can grenade the doors down, but the grenades must be very close