How to kill Neslug?

[FTF]

The normal preparations for this enemy are the same as all Monster Arena enemies: Hastega, Auto-Life, Celestial Weapons (as many as you can safely obtain), and your best armor. Overdrives such as Blitz Ace and Attack Reels work wonders (infact, if you do full damage with Wakka, two perfect Attack Reels will not only kill the first form, but also entirely skip the second), and Fury does well when inside the shell. Flare/Holy/Ultima work equally well against this boss.

Just to add on:
First form = 4,000,000 to 2,000,000 HP
Second form = 2,000,000 to 1,000,000 HP
Third form = 1,000,000 - 0 HP

Two 99,999 x 12 Attack Reels won't smash the shell unless accompanied by 7 other 99,999 hits before the second one.

If I remember correctly, pummeling it with Attack Reels will do damage while he's in his shell.

Attack Reels won't, but Blitz Ace will.