To unlock all characters, get a 100% game completion in Story mode.
Hueco Mundo conquest:
You can use Chad (normal) partnered with anyone else (Ichigo Full Hollow form recommended) to complete the first three conquests without any difficulty, excluding fights with Alon, Noitoria and Yammy Released form. When the battle starts, jump and do a strong punch (Circle). Then, prior to the opponent's fall to the ground, do three weak punches(X) followed by a strong punch. That should send the opponent flying to the other end of the screen. Repeat this and you should win with ease. If possible, equip Chad with Mayuri's Soul Code (seal opponent's strong, weak attacks and jump randomly after each attack). This works better if you combine it with the following method: charge your Reiatsu to maximum and, after hitting the opponent to mid-air, press SQUARE + TRIANGLE or use double special (after pressing L + R) prior to the opponent's fall to the ground, which must be timed correctly to hit. Chad (normal) alone is also quite useful for Stark's conquest as long as you repeat the above steps.