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.
I'm incredibly surprised no one has mentioned this yet, but the easiest way to get this achievement is by killing the berserker on Act 5, Chapter 7 (on the train before fighting General Raam). All you have to do to quickly kill her is lob a grenade at the fuel tank on one of the further back cars. The fuel tank will explode, and disconnect the car she is on, killing her and getting you the achievement. It's also worth mentioning that if you lure her into running off the back of the train you will not get credit for the kill (in other words, no achievement).
I did this in co-op several months ago and didn't get it. Recently tried again in solo and still didn't get it. I know I was on hardcore both times. When I was doing co-op my friend was on insane and I was on hardcore. Later we co-op'ed to finish my friends insane play through and we were both on insane fighting raam and when we beat him I got the beat raam on hardcore achievement. I think mine might be glitched ant suggestions on how to fix?
My boyfriend and I were playing co-op, on Insane difficulty, and when we beat the Berserker I got the achievement even though it wasn't on hardcore. The achievements stacked so you can do this on Insane so you don't have to re-play it once more.