The first part of this achievement is to complete The Green Hills of Stranglethorn. In order to do this you will need to do the following.

1. Head over to Stranglethorn Vale.
2. Locate Barnil Stonepot. Coordinates (35.8,10.5) and pick up the quest.

Pick up the following quests.

1. Green Hills of Stranglethorn - Chapter I
2. Green Hills of Stranglethorn - Chapter II
3. Green Hills of Stranglethorn - Chapter III
4. Green Hills of Stranglethorn - Chapter IV

You will need the following pages for each chapter. You can aquire then by killing the mobs in Stranglethorn Vale or by using the Auction House.

1. Chapter 1: Pages 1, 4, 6, 8
2. Chapter 2: Pages 10, 11, 14, 16
3. Chapter 3: Pages 18, 20, 21, 24
4. Chapter 4: Pages 25, 26, 27

Now you have completed The Green Hills of Stranglethorn quest chain.

The second part of this achievement is to complete Big Game Hunter. In order to do this you will need to complete the following quest chains first:

1. Panther Mastery
2. Tiger Mastery
3. Raptor Mastery

Hemet should now have the Big Game Hunter available. The quest suggests 3 players, but it can definitely be done with 2. Some classes such as a warlock or hunter can probably solo it. Hemet Nesingwary Jr. is located at coordinates (35.8,10.8). A few notes on Bangalash:

1. Bangalash is at (38,34) on top of the hill.
2. At 50% health he will summons 2 panthers that will fight with him.

Well there you go, another achievement complete for your toon.