Though I already finished the challenge, I'd like to explore some particular extra areas just to feel I finished my job.
Battled Zapdos at Power Plant;
Battled Moltres at Mt. Ember;
Battled Articuno at Seafoam Islands.
Azula is at level 63 and knows:
Blizzard / Bite / Double-Edge / Surf
So, that's it. I beat the game afterall, and completed the challenge. By the way, this was my first challenge, and I really liked it.