The achievement requires you to defeat dreadwood.
He can be located in Wierding Woods, which can be found via the Zombies HQ just left of the Changing Booth.
You will need to complete three 'main' quests which are in this area, called "Be Kind, Rewind!", "Becoming One With The Dumb" and "Zombie Prepared".
Once they are completed and you have the parts make your way to the Northern part of the map. Here you can constuct or place the Boombox.
Next a cutscene will shown three gates with hearts on them, I decided to go for the one that at the top of the map right where it shows the 'Boss Gate' icon on the map, not sure what the others gates are for or even do.
One progressing through the newly found area, make sure not get hit by the gusts, use the provided cover to weave inbetween the gusts.
As you approach the arena, turn on a sort of washing machine or transmitter that will turn on some jump pads to the upper area.
However, this is only for a limited amount of time.
To wake Dreadwood shoot the small heart on his back and the fight will begin.
It is quite easy and if you die he will not regain his health so you should be fine.
If anything is wrong or you feel it could be changed, please comment.