Chapter 8 in Bleach: The 3rd Phantom marks the first appearance of Ichigo Kurosaki and other familiar faces from the Bleach series. Its after this point that the main character you chose in the beginning of the game gets sent from the past to the present time and things start to really get good.
The first time you meet Ichigo and everyone, you'll be playing as them. Fujimaru and Matsuri are nowhere in sight. Instead, Ichigo, Chad, Orihime and Uryu are battling against some hollows and strange new characters called pluses.
Plus characters are basically ghosts, and will have a set number of turns in each stage before they become hollows. (This number decreases faster if a hollow is right next to them.) The way to save them, and gain a quick level, is to have a shinigami character purify them.
This is also the very first battle in which a bankai can be used. In fact, you'll probably need to have Ichigo use his bankai to prevent the pluses from becoming hollows. When Ichigo uses his bankai, his range of movement grows, he's more powerful and his sprite changes. This boost lasts for a few turns. So the first battle will basically serve as a tutorial for saving pluses and unleashing bankai.
You'll have to be careful here, since everyone is at a pretty low level. I'd suggest using Orihime mainly to heal, and having Chad and Uryu attack until Ichigo's able to unleash his bankai. Then quickly send Ichigo to save the pluses before they turn into hollows.
After Ichigo and his friends defeat the hollows, he runs off sensing more powerful ones and the story shifts to the character, lets say here to make things easier Matsuri. She has been rescued by Don Kanoji, and there's also a strange girl named Shiyo present as well. After a strange welcome and short introduction by Don Kanoji, Matsuri also senses the same hollows Ichigo sensed, and runs to offer assistance. The three of them find the vizard Hiyori with numerous hollows confronting Ichigo. So now Ichigo, one of the twins, Don Kanoji and Shiyo have to defeat them.
Don Kanoji and Shiyo are "guests" in this battle, which is a bit of a pain. The AI controlling Don Kanoji will send him charging after hollows even if he's near death, and Shiyo will only stay in one area and heal if a needy character is within her range. Since there are pluses in this battle (and Don Kanoji dying won't give you the dreaded Game Over), send Ichigo and Matsuri to save the pluses before they become hollows. Then take out the hollows at your leisure. You could probably even leave the pluses alone, since the hollows present will focus on Ichigo, Don Kanoji and Matsuri, but its better to just save them and level the two shinigami up.
After this point, Matsuri and Shiyo will go to stay with Urahara, and will then travel to Soul Society and stay with Kukaku Shiba. Once there, Matsuri will meet all of the Soul Society people from previous chapters, only all grown up and take part in a battle against Aizen and arrancar.
Images courtesy of Sega.