You can beat this thing in two easy steps, and you can essentially do it with Rikku and Yuna alone.

First things first though, before the fight, go back to the agency and buy 2 maps from O'Aka. Get Rikku and Yuna into overdrive. Now you're set.

Have your starting party be Rikku, Yuna, and whomever. BEFORE YOU DO ANYTHING ELSE, BE SURE EVERYONE PERFORMS AN ACTION TO GET THE AP AT THE END OF THE FIGHT!!! After that, Rikku should mix those 2 maps I told you to buy to make a beautiful Potato Masher, which will overkill the Negator. Yuna should go next, have her Grand Summon Ixion and Thor's Hammer the place up. Thundara it until it Mana Beams you, Ixion has exceptional magic defense and should survive it without Shield, you can shield on the turn before Mana Beam if you want to play it safe though. Thundara on yourself to heal and keep up the Thundara assault on Crawler. If you're lucky, you'll get into overdrive again before the fight ends. Use it for a wonderful overkill.