For challenge 4, try to have your Shield always move the same direction that the Dragon is moving, but keep it a slight distance away so that it can draw its fire, then move your Sword just into range and fire away. Took a few tries, but that was how I beat it.
@dragonknight88 you can only get some of the last row using summons. the rest you have to meet in the wild and have join your party. then theyre available.
Advancing is any easy way to gain points. Why not advance when you're guys are sitting around being bored the first 10 waves? You can easily grab an extra tp or two and get a more favorable landscape just by advancing.