The azure orb comes from that fight, so while it would allow you to complete the challenge, the only way to get it is to complete the challenge first. I guess you could hire one flying person to do the challenge once and then do it again solo, but that sort of defeats the point.
As far as the last boss goes, it wasn't actually very hard by the time I got there. Since you can keep pumping all your money into just the hero, you get some very nice stats. Using light bomb helped deal damage while keeping me away from the enemies. My light bombs were doing 99 damage, so the first two turns knocked out everyone except the two healers (Ravinale Protectors), the Elder Tig, and Zem. Next turn use feedback to heal up and kill one healer. Next turn light bomb kills the other healer. Then you just keep light bombing the crap out of Zem. I think this would be harder with any other element as you would have to get much closer to the enemies. I used the green and yellow orbs for increased speed (very important) and psy regen. I also had the golden orb equipped, but it didn't seem to do much for me; I guess it only regenerates health when you rest, which isn't often in the boss fight. For resistance, use either the black orb to make the fight before the boss a lot easier or crystal to make the boss easier.
Honestly, the hardest encounters were league 1 teams 3 and 4. At that point in the game you don't have any orbs, your health is low, and your attacks are weak. It took a lot of repeating the first couple of stages to earn money, then buy vengeance, then level vengeance to heal enough to make a difference. You also need enough health to take several hits. I think I did it with 32 or 34 health. I had leveled vengeance to return somewhere around 20 damage. It was also helpful to have mind blast + a full vengeance to be able to kill one of the bandit raiders (31 health on brutal).