I didn't really even figure out what the trick was to defeating the first Summon, but didn't have too hard a time of it.

For the second Summon i figured out what _seems_ like the right strategy during the first battle, but despite that i've not gotten my ass handed to me about six times so far =P

Edit: Okay, on the eighth or ninth try the strategy finally worked. I'd been trying the exact same thing for the last two or three battles, it's kind of annoying how much the result of big battles in FF13 depends so much on timing and where your characters happen to be standing.

It's also interesting that the target time after the battle was listed at 22 minutes, given that like all Summon battles i had a Doom timer :)