This is story related and can't be missed.
Make sure to equip each character with a feather accessory and/or earth gems. See below for more info.
Beware spoilers follow:
If you're following the walkthrough for the genesis version of this game, this boss won't be in it, so you might be slightly confused as to where to go once in Ludon. The boss and dungeon are new to the HD version.
Head to the inn (south western part of town after screen transition) and speak with the innkeeper. He will direct you towards a dig site to find your bounty. Head south into the hedge maze and make your way south; you'll come across a small house you can enter. Enter and go down the stairs. You'll be in the basement which is the same design as the hedge maze above. The light will flicker on and off; you can either wait to move in the light or bring up your menu which will temporarily remove the darkness allowing you to more easily move in the dark.
Head to the north eastern part of the basement towards stairs that appear to go nowhere. At the top of the stairs move right through a hidden passage in the wall. Go down two more sets of stairs and you'll be in the rock cellar. This dungeon is very straightforward; moving in a southerly direction you'll quickly come across a save point, the boss is just after the save point.
The boss has roughly 2000 HP and attacks with the earth element. Feathers (50% earth damage reduction) are preferable over earth gems (negates 5 turns of earth attacks then breaks) but either is fine. He also has some amoebas with him and can summon more ( each amoeba has roughly 900 HP). For this battle we'll be using Edessot and Zellini as our primary attackers with Kruller and Hoston serving as gather batteries, and Alina healing. If using this strategy, move Edessot and Zellini to the back row prior to the boss to lower the frequency of being hit.
Have Hoston and Kruller keep Edessot and Zellini as high a gather level as possible. Reminder: at gather level 3 or higher you can lose a level of gather if hit by the enemy. Have them cast fireball and lavafall every turn. If you can spare the gather, getting Alina to gather level 2 is helpful. Once the main boss is defeated, the rest of the enemies will flee.
You will be immediately transported out of the dungeon so make sure to grab any chests prior to starting the boss if you want to avoid additional back tracking later.