I read this on a gamefaqs.com FAQ, courtesy of Ultima Gamer and CB!:

So, three characters (one being Wakka) need to have 255 strength so that they can hit for 99,999, and full overdrive gauges. Neslug will retreat to its shell when it has lost 2 million+ HP, where it is resistant to all weapon based attacks (including Passado). So, start the battle with a Hastega. Have Wakka use Attack Reels, getting all 2s. Then use Quick Hit 8 times. This is a total of 20 hits at 99,999 a piece, which adds up to 1,999,980, just shy of 2 million. Now Entrust to Wakka and perform Attack Reels with all 2s again. This will be enough to break its shell before it has a chance to retreat. Now, have someone perform Silence Attack to stop it from performing the very evil Slime attack, and kill it quickly.