General Vermin is a special rat commander who uses its size and strength to crush its enemies. He first appears in the Game Boy game as the boss of Stage 7, using a mace as his main weapon.
In the arcade game, General Vermin appears as a type of grunt enemy. The Battletoads first fight them in Stage 3 and later Stage 5. Given how multiple Vermin appear at once, it's more likely that "General Vermin" is a type of rank for some rats, and not a specific name.