When I first fought the Ch9-Boss, I got completely wiped out by Destrudo. So I thought the only way to survive is to summon an Eidolon and go into Metamorph Mode due to the invulnerability you gain. Of course, I was shocked to see him cast Destrudo a second time so I got pissed off and attacked him and prepared myself to be wiped out. Fortunately, Lightning had enough HP to survive the weakened Destrudo. And that's how I discovered that you could weaken Destrudo.
Well, I beat him on my second try, so now I'm off to Ch10, just started and went through the Arc three times to collect some CP. Wtf is up with the extra-high CP cost for the new classes !?