Neslug has three phases:

Out of shell
In shell
Without shell

The first part should be relatively easy. Attack and revive as necessary. In the first and third forms, Neslug will use a normal attack, which does random damage, Megaton, which causes Poison, Curse, Armor and Mental Break, and does heavy damage. It also uses Slime, which dispels Haste, and does damage to all enemies.

The second form is the most painful of the three, where it recedes into its shell, and begins a long process of healing itself. During the time, it is Immune to Physical attacks. It has Auto-Regen during this time, which will at first, heal for only 100 damage, then it will jump sky high. If it gets a turn, it will use Curaga on itself for about 8k, but Regen also works on that turn, which means it will heal something in the area of 50k+. If you don't do enough damage, then it will come back out of the shell, and you'll basically be doing the first part again.

The third part, the Neslug is more likely to cause 99999 damage when using its attacks. You will know when you have reached the third stage when you see in battle that the shell of the Neslug has been completely destroyed (it blows up, to put it in simple words).

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.