@thedestroyership A summary from what I understand:
Following the Jailbreak arc, this group of girls used it as an opportunity to break one of them out of jail and identify a really skilled hacker (Uihara). Thus, they try to kidnap Uihara to reveal the Power Development Curriculum and spread it, hopefully allowing other places to create espers. Battles ensue, and ultimately Uihara is saved.
The real confusing point is the "main villain", Shundan Kimi, and her weird abilities. She herself has an esper ability that allows her to create black holes (Level 5 potential, but recorded at Level 0 because they didn't understand it at first). The black holes she makes have huge amounts of energy, which attracted the "angel dragon" (possibly from Touma's Imagine Breaker) which basically became a parasite and leeched off her ability's energy. She could somewhat control the dragon through her esper ability, giving a whole set of weird powers (salt manipulation, sand creation, power copying, mind control, etc). Eventually the dragon nearly took over her though.
How did she get freed from the dragon? They didn't explain it well, but this is what I interpreted it as. Uihara, in a combination of absolute desperation and determination, pushed her mind and AIM field to its limits to save both Saten and Shundan. By reimagining the way she interprets the world (and thus her Personal Reality), she was able to redesign the mechanisms of the long-range AIM jammers in the area, making it compatible with the dragon (which shouldn't have be affected by normal esper/AIM related abilites). Thus she was able to "jam" the dragon and force it out of Shundan, saving her and also everyone else that was affected by the dragon. The dragon is almost 100% not dead though, just got its power temporarily depleted, so who knows where it is now (back to Touma?).
Ultimate point of the arc is sort of crudely executed, but can be seen as:
Being strong and being a hero are separate things. Being saved doesn't make you weak, and being the one saved often takes strength that is hard to recognize.