Grenades are sold at the Al Bhed shop right before the fight with the Crawler.

There are many different ways to bring down that negator besides Wakka's ball. You can bring in Rikku who will use Grenades (they target both the Negator and the Crawler), Wakka's ball, obviously, and Kimahri's Lancet (although it doesn't do much damage, it's better than nothing I say).

Before the big boss fight, train on the fiends just outside the Al Bhed shop. Bring Yuna's, Lulu's and Ixion's overdrive to the top. Once the negator is down and out, bring in Lulu to cast her overdrive, Thundara Rage, bring in Tidus to cast Slow on the Extractor (or use Tidus' slowtouch weapon bought at Luca at the beginning of the battle) and then have Yuna summon Ixion. Pay attention to the CTB bar. Perform an attack/overdrive, up until the Crawler says 1 turn left until mana beam. When that happens, heal (if you need to), and you MUST use Shield on your last attack before the Mana Beam. It will do a measly 200 damage if Yuna has been properly trained. Heal yourself with thunder, and attack. Don't let the Crawler get two attacks in a row when it has one turn left before the Mana Beam. In fact, don't let the Crawler get any turns in a row.