To begin, I completed half of this achievement on the Xbox 360 and the other half on the Xbox One. However, I imagine the quests are identical across both platforms.
This questline consists of several quests which in turn, each have several parts. The first of these quests becomes available upon completion of the “Taken King” questline. The “Taken King” quests are fairly straightforward and you can reference the “Taken King” guide if you have any questions.
After defeating Oryx and reporting to the Titan Vanguard you can speak to Cayde in The Tower to receive the first quest in a line of four called “The Taken War: Earth.” The bulk of this quest involves killing a Taken champion in The Divide, Rocket Yard, and Skywatch on Earth. The champions only appear when patrolling, not during missions.
Here is a link to a website that provides a map and videos showing the route to most locations within the game. http://destinypublicevents.com/
To summon the Taken Champions, you must hang out in the prescribed areas until Taken forces show up. The sky will get dark and a message at the bottom left of the screen will announce the arrival Taken forces. These events are time based and as of the writing of this guide I do not know of a way to predict these events or of a method to speed them up. Once the Taken arrive you must kill 3 Taken Lieutenants to draw out the champion. A message in the bottom left of the screen will announce when a lieutenant arrives and is killed. Lieutenants are the Taken form of each race’s elite units (either a Fallen Captain, Vex Minotaur, or Cabal Centurion) and are the only taken I’ve seen with shields. Finally, shortly after the third lieutenant is killed a message will announce the arrival of a champion.
The champions are Taken form of each races ultras (the big guys typically serving as bosses of missions, strikes, and raids) whom by themselves are not terribly difficult to fight. The problem is they have a never ending supply of taken lieutenants who spawn at their feet. Concentrated fire from these lieutenants is far more dangerous to Guardians than the actual champion by himself. Each champion is about twice the height of a normal bad guy so the easiest way to kill these champions is to place a piece of terrain that is waist high on the champion between you and him. This allows you to fight the champion without having to worry about heavy fire from the lieutenants.
For example, on Earth in the area called The Divide the champion often (not always) spawns between the two large orange shipping containers near a building. There are several locations within The Divide which allow you to shoot his head and shoulders and do not allow the lieutenants at his feet (in between the containers) to shoot at you. Once you find a good spot the only challenge then is killing him within the time limit. This will likely require 3-4 high level guardians to deal enough damage.
After killing all three champions you must complete a mission called Kings of Decay. This is a mission similar to a story or strike mission and is accessed from the Set Destination button while in orbit. Compared to the Taken champions this mission (and similar missions associated with the other quests) are easy and straightforward.
After reporting to Cayde following the Kings of Decay you can report to Zavala in The Tower to receive the next quest called The Taken War: Mars. The most time consuming step of this mission is step 3 which requires you to kill 6 Taken lieutenants on Mars. Again, nothing difficult, just time consuming as you wait around for the Taken to arrive. Once they are dead you are assigned another straight forward mission.
Next you receive the quest called The Taken Wars: Petra which is almost identical to the Taken Wars: Earth. Each step sends you to a different planet to kill a number of Taken Champions. The only difference is that during each step one of the champions you kill will drop a piece of battle wreckage that you must pick up as part of the quest. Once you kill all the necessary champions, get the gear, and give the appropriate people the right amount of attention you receive the final quest for this achievement titled The Wolves of Mars from Varik in the Reef.
First you must kill about 300(ish) Fallen on Earth, the Moon, and Venus. Nothing tough, it just takes time. I found the best places to farm are the following:
Earth – The Divide
The Moon – the area you spawn in when you begin patrolling.
Venus – The Ember Caves
The next step sends you to Mars to kill a Fallen Archon in the Rubicon Wastes. Patrol to the Rubicon Wastes. Much like the Taken, at certain times a message will declare the “Wolves are on the hunt.” This will cause Fallen dropships to begin sending troops to the map. Simply kill enough of them and a big Fallen, the Archon, will appear. Kill him and return to Varkis. He will give you the final mission titled a New Den. Again, a structured mission with a boss who is easily beaten. Once you kill the uber-servitor talk to Varik and the achievement is yours.
This was a long quest line and I did my best to take accurate notes while playing through it. If there are any mistakes or if you decide to give a negative vote please comment or PM me so I can make the necessary corrections.