In order to earn this trophy, you must be playing the zombies map Ancient Evil.
This trophy can be earned on any difficulty, so if you are having trouble with this, try it on Casual.
First thing you want to do is opening doors and get to the theatre to obtain the Sentinel Artifact. Once you have obtained it, you can now start the challenges towards the Eternal Flame.
Right where you spawned, there will be a bowl in front of the Oracle. It will ask for 500 points as a tribute. Offer the tribute and the challenge will appear on your screen with a countdown for it. You must complete enough of these challenges in order to reignite the Eternal Flame.You don't need to collect your reward from the challenge right away
, you can continue to do challenges to upgrade the reward.
Each reward you earn for the challenges will count as points towards the flame when you pick it up.
Common - White - 0.5 points
Rare - Blue - 2 points
Legendary - Purple - 4 points
Epic - Orange - 6 points
In order to fully reignite the Eternal Flame you will require a total of 9 points, which is basically 1 Legendary Reward and 1 Epic Reward.
Simply complete this and the trophy is yours.
Tips: Don't advance the rounds if you don't have to. If you have a take no damage
challenge, save a last zombie and just run in circles. Same thing if you get a hold such and such location
Here is a video I found on Youtube showing the process