This achievement requires you to first understand how challenges are issued. The game tracks specific statistics:
Number of Kills in Gametype X
Long Distance Kill
XP in a match
Kill X number of (scouts/rifleman/engineers) in a match
Conflict Objectives in a match
In order to get a challenge from a friend - they must have a higher score (or the same score) in one of these statistics as you do. So if you've gotten 10 headshots in one game - you will never get a challenge for headshots from a friend who has less than 10 in a game. In other words - if you are good at the game, and play it a lot - you reduce your chances of getting any friend challenges at all!
So - to make this easy, you want to avoid building up any of the statistics listed above to make sure you get easy challenges. If like me - you already have high stats - Ubisoft just reset the Challenege statistics in August and has promised to do so regularly (prob every 3 months). After a reset - you will only get challenges from friends who have completed at least one online match since the reset occured.
Once you do get an easy challenge - accept it and get the amount you need to complete the challenge - and no more. Becuase your friend will have to beat that score by one, then you have to beat their score by one, and so on.
So if your challenge is get more than 0 melee kills in a match. It will go like this
You - Get 1 melee kill
Friend - Get 2
You - Get 3
Friend - Get 4
You - Get 5 - achivement unlocked.
Also - note that each time the challenge is volleyed - you have 24 hours to accept it- but once you accept it, you get less and less time to complete it.
1st Round - 24 hours to complete
2nd Round - 12 hours
3rd Round - 6 Hours
4th Round - 3 Hours
5th Round - 1 Hour
As you can see - on the last round, you get only one hour - so make sure you play at a time of day when lots of people are on - so you can find a good map and match for your challenge. And if you want friends to help you - party up and get in a lobby before accepting. REMEMBER - you can accept the challenge from the pre-game lobby once the map vote is locked - so you can wait till you get a map you like before taking that last challenge on.
Also, its possible your return fire volley and your friends normal daily challenge could end up being the same thing - but if they accept the wrong one - it messes up the achievement. So look at EXP values to make sure you have the correct challenge, they are worth 500, 1000, 1500, 2000, 2500 depending on which volley you are on 1, 2, 3, 4, 5 respectively.
Only the person who did the first challenge gets the achievement - so when going for your challenge, you ideally want to only work on what you need to complete the challenge - if you do lots of other stuff in game - you are raising other statistics - which means all future challenges will be more difficult if you fail, or if your friend wants to get the achievement later, your challenges to them could be too hard.
You MUST FINISH THE MATCH to get credit for a completed challenge. But - if you are not going to get it in a game, and you have a bunch of other stats you may have increased - you can quit out before the end of the match and none of those stats will be saved. So before a match ends - if you don't want your stats stored and you won't beat the challege - just quit. This ensures you can keep your stats low until you beat the challenge.
If you have a second account, that makes it easier to coordinate getting all the rounds done, since you can do it all yourself - but the second account needs to have beaten you in a statistic for that account to issue a challenge to your main. The nice thing is, you can see what the challenges are to that account from your main - and that is basically telling you what your high score is in a statistic. If you tie that score with your second account - it can then issue a challenge for that to your main account.
Just make sure you pick a challenge you think you can beat by 5 or more points in one hour for the final round (i.e. avoid conflict objectives and data hacks). The best challenge is for X number of kills in a match because there are no conditions on how you can get them.