If there ever was a mislabeled achievement name, this is it. All of the "impossible" challenges are insanely easy to complete. This is due to the simple fact that you can play these challenges on whatever difficulty you would like.
To access the Impossible Drum Challenge you must play through all of the subsequent drum challenges in the challenge mode. These are accessed from the same menu that Band World Tour can be accessed. When you beat a drum challenge, the next one will appear in the next challenge tier. If you know someone who has this challenge unlocked already, simply play the impossible challenge online with them. You do not need to play all of the challenges, just the impossible one to get the achievement.
This is simply a matter of putting in the time as easy drumming is, as it's name would suggest, VERY easy. You shouldn't have any problem beating all of the challenges, including the "impossible" challenge on easy. If you do have some problems, remember that focusing on the bass pedal and the red pad is the key. If you are having trouble with a complex beat, just focus on the pedal and the red and you should make it through fine. You can also use the freestyle sections that you get when you have a full overdrive meter to take a break for about five seconds. This is an invaluable tip for getting through long or especially tough songs. I don't think you will need any of these tips on easy, but if you do have trouble just keep at it. Practice makes perfect on drums.
You can also tag onto someone else to get these achievements. Simply play the Impossible Drum Challenge with a friend on drums with you playing the instrument of your choice. If you do this, you will also get "Along for the Ride" at the same time.