The normal Anything Eater has access to powerful magic, such as Flare and Osmose, which the oversouled Anything Eater does not. Its spells cannot be reflected because its casts them using its own reflective shield. It has one physical attack.
For its oversouled state, Anything Eater may start picking off party members one by one depending on dressphere. It no longer has Auto-Reflect, but it can dispel the party's Reflect.
One can opt to use brute force, because at this stage of the game an enemy with 36,980 HP and 38 Defense isn't particularly tough, especially when Anything Eater is vulnerable to Slow.
Equipping Tetra Bands, Tetra Guard, or the Tetra Master Garment Grid helps because they either nullify or absorb elemental spells. (Tetra Master needs a round of dressphere changing.) Using Reflect is not recommended, as the normal Anything Eater bypasses it by casting spells on its own reflective shield and the oversouled Anything Eater dispels the party's Reflect before casting spells. While this can be remedied by equipping a Star Bracer to maintain a permanent Reflect effect, it only has marginal effect as the oversouled Anything Eater focuses more on physical damage.
If Anything Eater is oversouled it is best to avoid having all party members with the same dressphere and to spherechange whenever the message "Me no like dressphere!" appears.