I finished the last of the story missions today. They were entertaining, but when I look back and try and sort out the narrative, it occurs to me that there isn't actually much of a story. I think the issue is a pragmatic one. When you play a pickup game of online coop, there's no telling what levels the other people might have played, so a self-contained mini story can keep everyone on the same page. And if you play coop a lot, being able to shuffle your level order will help to keep things from getting stale. The best way to think of the missions is as episodes from a syndicated cartoon show, where the end of each episode resets to the status quo.
The status quo, as far as I can tell, is that a malevolent and mysterious forces has entered our universe and swallowed all the stars in the sky . . . except one. Solus is the last unconsumed star and the object of a long and bloody war between the forces of Rendain, who wants to help the invaders (for no reason I can discern) and everyone else, who want to stop him. Episodes 1-7 take place some time in the middle of this war and could be separated by hundreds of years for all I know. Episode 8 is probably at the end of the story, seeing as how you finish by killing Rendain, but the threat of the extraplanar invasion still remains, so maybe it's not actually the last chronologically after all. If I play through them again, I'll have to pay attention to that.
It's not super important, though. In a game like this, the story is always a thin excuse to kill tons of enemies and horde tons of loot. By that standard, the Battleborn story is a success, providing some humorous banter to distract from the necessary grinding.
Speaking of which, my next move is to try and unlock as many of the remaining characters as possible. I still have seven left to go, and I'm fairly sure that I can unlock at least two before my 20 hours are up. The rest are theoretically possible, if I were a lot better at the game and could reliably get silver medals or better on the story levels, but realistically, I'm only getting them when I grind my command rank to 40 (it is currently 13). That's a shame, because the thing I love most about this game is the characters, but it's all right, because I expect that I'll be playing Battleborn intermittently for years to come.