I'm not sure, but I think you'll have to finish the game again to start a new Real Disaster game. Or you could get back to your first run's final stage save and get the 10 missing titles before you start a second run.
Real Disaster is just harder than the other modes. You do see it on screen though, as escaping the disaster will always be a much closer call than before. Also, you're arms will fall off during running sequences (I really hurt my arms with the one at the start of level 18).
Replay the first mission, it's pretty easy to beat without taking any damage. It also not too hard to get and S-rank there.
Getting E is easy but long. Use some assault rifle or the gattling gun to lower your precision. Be sure to make the fights very long (by hiding all the time, or not if you play on Normal). Get near death a lot. Avoid combos and head shots... Basically, check the different ranking categories at the end of the stage and be sure to be terrible at every one of them.
