(Edit 10/1/18) I have had some people tell me that this achievement is giving them some troubles in regard to unlocking. TrueTophies states that the third milestone has been completely removed from some players as of right now due to the release of forsaken. This would not be surprising as the trials of the nine achievement is also unobtainable as of right now. I don’t play the game as much anymore, so please leave in the comments if it becomes obtainable again in the future, which it should be.
You get this quest as soon as you reach the farm, one of the new social spaces, and talk to Shax. Access to the farm, happens pretty quickly into the game. There are three parts to the quest: (1) complete 2 matches in the quick playlist, (2), complete 2 matches in the Competitive playlist, and (3) earn glory by participating in the crucible. This last step is what I want to get into. You can do this in both quick playlist and competitive, but I would recommend quick playlist as it is easier going. You will notice that the step is connected with a percentage. Through my calculations, getting two kills (assists count) will net you 1% and completing a crucible match will net you an extra 2%. To give you an example, this is what my first game looked like
Opponents Defeated: 24 kills/assists plus the match completion=14% (That is 24 divided by 2 is 12% plus the extra 2% giving me all in all 14% for the first match. This took me around 2 hours of playtime, but it all comes down to how you are in crucible.
After reaching 100% on that step, return to the farm and talk to shax to complete the quest. (If the achievement doesn't unlock, just go to settings and hit change profile and sign back in. Once you reach orbit, the achievement will unlock). One thing to keep in mind with this achievement is that with the weekly reset that occurs in destiny 2, all the weekly milestones will reset. This quest is one of those milestones, so if you are at 77% progress and you don't finish it before weekly reset, the progress will reset for the week. So heads up, try to get this done in a week's time.
Edit 1: It seems that some people are having a hard time with having the achievement pop. The guide says exactly what to do for the quest and what to do in case it doesn't pop. I don't know if it is a glitch, so it may be an issue on xbox's end, but the solution is correct. (A way that could help for those having issues with the achievement popping is trying a crucible match or two after you have turned in the quest to perhaps trigger the unlock.)
Edit 2: With a recent update to the game, this achievement is now much easier to obtain. I have not tested out the exact precentage of kills, etc.. but you will be able to finish this in much less time than as before.