OK, it sounds like in general you're doing the right technique. Kill the negator first, then bring in your aeons one by one so each one takes a mana beam and dies. Are you sure when you bring in the aeons that they are coming in at full level and do their full blast right off? Dismiss your strongest one so they don't die. Then if you have Yuna at grand summon level she can summon that one back for a second powerful blast.
Is that what you're doing, or did you forget to get them all charged up?