Edit for 2017:
Now that most workouts are gone, I suggest using the Demo against a 2nd account. Get very low scores with your 2nd account, so it will be easy to beat. If you keep matching with real friends who are too hard to beat, you'll need to temporarily delete them until you start matching with your 2nd account. The game seems to match you with the same GT over and over.
To get this done as quickly as possible, you can rewind a drill until you get a yellow Challenge. Hopefully it's a Friend Challenge. Once you get a Challenge for a drill, you won't get another one for that drill until you finish the workout, go back to the main menu, and start again. It also seems that the first one or two drills rarely have Challenges. When using the Demo, I would fast forward past Tony Horton, then rewind Jillian Michaels until I got a Challenge, then move on Anderson, etc. I also never got a challenge at the end for Yoga, so I suggest skipping that too.
Previously glitched, but apparently working now. More comments about the glitch after the solution.
You only need to follow a gamer for their Friend Challenges to appear. They do not need to follow you back. Use the Friends app or X1 SmartGlass to Add Friend. You will automatically become a Follower.
XbAndy360 was successful using a 2nd account as his friend. Keep in mind that 2nd accounts have Gold privileges as long as your main account is Gold.
When your friend does a workout, an announcement will appear in the Messages feed (bottom center of the main menu). Do the same workout and hope to get some Friend Challenges. (You don't need to use the Messages feed. This is just a way to know what your friends have done.)
Challenges are random, so you may or may not get any, especially with a 10 minute workout. I've had as many as 2 on a 10 minute workout and 5 on a 20 minute workout, but I've also had 0.
You will either need to beat their best Fitness Points, average Fitness Points, or best Star level during a drill. Since the Stars max out at 5, these are the easiest challenges to win and you only need to tie.
Achievement will unlock as soon as the 10th Friend Challenge has been won. All 10 challenges can be against the same friend or a variety of friends.
Feel free to follow me, but please don't send Friend Requests over xbox.com or 360 so that my 360 Friends List does not get full. I have intentionally done poorly on:
10-minute Solutions - 5 Day Get Fit Mix:
Belly Fat Burner
Fat Blasting Intervals
I will probably need to really do these workouts eventually for Fit-Ness Monster, but I will avoid them for awhile.
Regarding the previous glitch:
Please comment if your progress is still stuck at 10% in the Achievement app. I was reset from 10% back down to 0%. Xbox Fitness also refused to start any workouts, crashing back to Home. I had to do a deep shutdown of the console (hold Power for several seconds) to do workouts again. After this, my progress worked as it should. The deep shutdown may be unrelated, but I put it out there in case it helps others.