Sadly its more of a fighting game than a Dragon Ball Z Story, the story mode is basically a fighting arena. You jump from one fight to the next. You'll need to have watched DBZ to know whats going on.
In the “Story Mode” there are easy battles and then really hard battles. Some of the hard battles is where you have to evade your enemy for 60 seconds without dieing. 2 or 3 beam attacks from your enemy will kill you, you wont be able to lay a scratch on your enemy, and whats worse is you'll find it quite hard to dodge out of the way of your enemys attacks.