1. Story Mode: Progressing through the Story Mode will unlock numerous characters. As you advance through the main storyline, completing character arcs and specific missions will grant access to new playable fighters.
2. Dragon History: The Dragon History menu showcases various story scenarios and events from the Dragon Ball Z universe. By clearing challenges in these scenarios, you can unlock hidden characters.
3. GT Mode: Similar to Story Mode, GT Mode revolves around the events of Dragon Ball GT. Completing this mode also unlocks additional playable characters.
4. Bonus Mode: The Bonus Mode presents challenges and rewards. Some challenges, like the Z-Battle Mode and the Character Trial, award characters upon completing specific objectives.
5. World Tournament: As you participate in the World Tournament and achieve high rankings, you'll earn points that can be exchanged for unlockable characters.
6. Unlock Codes: Some characters have specific unlock codes that can be inputted at the character selection screen. These codes are often found in game guides, magazines, or online resources.
Remember, some characters might have complex unlock conditions involving multiple steps or achieving certain criteria within the game. It may take some effort to unlock all characters in Dragon Ball Z Budokai Tenkaichi 3, but you can gradually access the entire roster by following these methods.