(EDIT: For those that have voted negative on this, I'd like to ask for your input in the comments as to why that was the case. If you feel there was something missing or that may be better, I'd love to hear it! Otherwise, I can't improve this solution for others to make use of, or give credit for whatever input you may have.)
There are two Dream Battles that require you to complete their Special Challenge by not taking damage throughout the battle, so you may choose to attempt this while completing these challenges for the Sweet Dreams
Challenge 6: Justicar's Judgment, and Challenge 16: Blades and Bones, require that you do not take damage in order to complete the Special Challenge. These can be somewhat challenging, given the large amount of enemies that will follow you around or shoot at you, like the Cactuars or Killer Bees.
Challenge 13: Slithering Surprise, however, may be the better option if you're having trouble with 6 or 16. Challenge 13 is filled with Midgardsormrs, ground-burrowing snakes that pop out of the ground to bite you. These enemies are slow, and fairly easy to avoid, with a small amount of Ronin and Goblins trying to get in your way otherwise. Focus on taking out everything but the Midgardsormrs, and feel free to be very liberal with your companions' attacks when they become available (I would suggest Cid, with
, or Clarus with
) to clear the area when things get too hairy.
I would also recommend using Ice magic to slow enemies down; there are a lot of them at times, so you can potentially hit a good few of them and make your attempt far easier. Remember to time your dodges (
) for when you really need them, and you should unlock I Dream of Awesome
at the end of a successful attempt, during the results screen.