Easy Level Up
Getting your character to a high level can take some serious time and effort. Luckily, there is a much easier way to go about this. Start a game in the Dragon Universe mode and head to Kami's Lookout where you first level up. Save your game after and immediately quit. Start a new story and repeat the process as many times as you wish.
Free Capsules
Capsule items allow you to use certain bonuses during battles and can also unlock certain characters and moves. To get some free powerful capsules, use a memory card to save your game that has a "Budokai 2" save file on it. When you start your "Budokai 3" game, you will have the character Bardock's capsule, Bibidi's Pot capsule, and the Silver Membership Card capsule which can be used at the item shop.
Alternative Stages
While this cheat doesn't necessarily make the fights any easier, the alternative look of each stage completely demolished does have a certain aesthetic appeal. To play on each stage's destroyed alternative, press the Circle button instead of Square to select the stage.