There is a very easy way to do this:
First Level Wakka and Yuna up as high as possible, these two are essential for this fight, try to get both in Overdrive as well before the fight but it doesn't matter if you can't. When the battle starts immediately have Wakka focus on the Negator while having Yuna heal for the time being, once it's dead, wait until the counter for the Beam get's to 3. Then summon any Aeon (Ixion would do), and do not attack the cannon; when the counter goes to 2 immediately start attacking like mad (This is the only time the cannon can't counterattack) and eventually when the Beam Cannon come's it should kill the Aeon and not your team, by this time you should have over 5 Aeon's, if their all in overdrive then the cannon is doomed from the start.
Continue that strategy and you should win.
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