Have a friend complete the 1st wave in a challenge and die in the 2nd wave. Complete at least the 2nd wave and bounce it back and have them fail it. Repeat 10 times. The achievement pops at the bounce back on the 10th challenge, soNdox2 has confirmed the bounce back is necessary.
This can be done with a single friend you don't need 10 different ones.
Any challenges you send that get failed do not count towards this achievement.
Note: Any challenges done prior to the July 27, 2012 title update do not count towards this achievement.
This is based on my observations. I had 9 challenge wins before the title update. I won 12 challenges afterwards, 2 were one I sent that got failed, the other 10 were sent to me which i passed and bounced back. All of the post patch wins were with the same friend.
EDIT: Based on the experience of Fire Hawk D in the comments: If the achievement doesn't pop after 10 wins doing this, try waiting a day and trying again. It seems there may be a bit of lag for the stats to count.
EDIT2: As UnafraidComic44 noted in the comments if you're using an alt account that's on your friends list to do this make sure to go back to the dashboard when switching between the accounts, don't sign out of one account and into the other within the game. I had two controllers logged in and dashboarded to switch between the two.