There's only three flashing boxes...one on top, one in the middle, one at the bottom. The room scrolls, though, so it gets REALLY confusing.
That's the fight with Dekao....you have to run after her as fast as you can (avoiding her timebombs) and try and do some damage to her (preferably with a full punch combo or the R trigger/Laser EX skill) - as soon as you stop hitting her/end your combo, she does a little dance and turns invisible, keeping you from hitting her (I think). That may wear off over time, but what you're supposed to do (I believe) is hit each of the flashing reactors or whatever, and she'll become visible again.
She also seems to become visible if you use the L trigger/Machine Gun EX skill, as long as she's on the same screen (the only way to tell with this is to watch for her to drop a fresh bomb).
Basically, beat on her while she's visible, take a breather while she turns invisible, then do whatever you can to make her visible again.....repeat until she finally bites it.
I'm currently trying to figure out what the hell is up with the character/new game system....I was going through my game again, trying to figure out what was new, and not much seemed to be (a few extra convos here and there, some hidden characters I hadn't gotten before).....but then I got to the mission where you're in Antartica (I think), and instead of that twit Rug being in charge, it was Rock/Deadcross, and there was a Black Look with him! (as well as Lamp, but Lamp gets around, you know?)
Boggles the mind...