Bonus Objectives and the demo...
Well, I've now been playing the demo and killing myself at the last part of the stage over and over for up toward an hour. Going back down (heck, you can just jump down and land on the lower platforms if you wish) and even all the way back to the door to the hangar (it closes once you leave the hangar) respawns quite a few of the enemies. Their spawning is triggered by walking past certain spots and when you die, they can respawn again.
This means that killing yourself allows you to replay segments and thus get way more style points than you usually would.
After the third levelup of Starkiller, I got a bonus red sphere for clearing an objective.
It didn't say WHAT objective, but it said I cleared a bonus objective and I'm guessing it's either "gain # levels" or "kill # enemies".
I figured I'd share. I've now leveled up 5 levels and counting xD