If you're new to the concept of these kombo challenges, try out Batman or Jax for starters - those are two of the easiest ones in the game, but they are by no means "easy" unless you've got a firm grip on the combo system found here (and also used to the touchy controls and weird timing).
If you can fly through those, great! Keep moving on through the various challenges, remembering to take a breather now and then, and have something handy to punch when you get stuck on something (and you will get stuck on a lot of somethings, trust me). If you have trouble with those two, keep practicing - you'll eventually get it. If you keep practicing and still can't do it, you might want to pass on this achievement.
Judging by TA scores, a list of characters in order of difficulty (easiest first, hardest last):
Shao Kahn (you have to beat the MK side of story to unlock him)
Darksied (you have to beat the DC side of story to unlock him)
If you get stuck on a particular challenge, check out dec1Bel718's videos on YouTube:http://www.youtube.com/user/dec1Bel718
He shows you exactly how to do every combo in the game, and unlike the other videos, he actually tells you the timing to use, tricks to make them easier, and other nifty pointers.
One last tip: if you manage to finish every challenge in the game and this achievement doesn't pop, double check all of the characters. There's a known glitch where random challenges will reset, so you may have to go back and do a few again... personally, I had to redo all of Wonder Woman and half of Deathstroke even though I had already finished both and got the individual achievements.
Xealon replies to the above: "The reason they are resetting is because you are exiting the game directly using the XMB. If you go to the character select screen before exiting you can avoid this."