Really, this story trailer speaks for itself. Look at it! Watch it! It's so cool!
Alright yeah there's more to this story. Many have been expecting Umbrella to be the eighth character in Skullgirls, but this trailer hints at Umbrella being a recurring story character rather than being playable (at least initially). If she is indeed Parasoul's younger sister and Parasoul is the previous Skullgirl, that would make Umbrella pretty important as well. Now there's no confirmation here, all speculation indeed, but the silhouetted figure at the end of the trailer is more likely the eighth character. Hopefully she's not some overpowered v-13 (Blazblue) character or something to that extent. Either way, the story mode format seems to follow a traditional fighting style fight-by-fight mechanic with dialogue-based character interaction between fights. Who knows if it's voiced over, would be nice though.
Source: PlayStation Blog