(Keep in mind that the unit and weapon suggestion sections are partially subjective due to my experiences with the fight)

Ok, this battle is quite simple and all you'll need is some basic stuff.

The boss is Burning Soul Balamgram and can be quite hard, depending on your circumstances.

He'll use AOE attacks that have a chance to poison/curse you, so be careful.

Every 5 turns, guard all of your units, Balamgram will use "Vindictive" which, if you don't guard, will reduce all your units HP to 1 regardless.

Every turn (that I saw) he'd at some point use a random target attack on your units, if you have a BC on hit buffer like Laberd or Soleil, you can basically get all of your BB gauge back.

At 75%, Balamgram will buffwipe your units and buff himself with an Attack boost, Dark Element, and a probable Curse effect. Normally, his attacks don't hurt that much, but with the attack buff he gets, that changes quite a bit and he starts hitting like a truck. You can, however, counter it. If you deal about 5% Light Elemental damage to him after this buff, he'll buffwipe himself and won't do as much damage anymore. He does the same thing again at 40% HP, but you need to deal 10% Light Elemental damage this time instead of 5%.

At ~15% HP, Balamgram will use a very powerful single target attack on some of your units, it's advised to either sacrifice a unit to put him below 15% HP and guard all, or you can have a mitigator like Laberd to greatly help by using his BB at the threshold for the 50% mitigation buff.

Then all you need to worry about is Balamgram's "Vindictive" attack every 5 turns.

Advised units are Laberd, Eclise, Rigness, Soleil (that I know off the top of my head).

Laberd has BC on hit, a Defense buff, and 50% mitigation, all very useful in SArc. Eclise has Status Ailment Negation, buffs with Light/Dark elements, and burst heals, quite a good kit. Rigness_ at both 4 and 5* heals, negates ailments, and cures them at the same time, which is very solid. Soleil's BB has burst heal, ailment cleanse, not negation, which is one of the best optimized buffs to have while fighting Balamgram. Soleil can still do good though, so try her out if you can.

Now for the weapons and LS spheres.

Probably one of the best weapons (and probably for a while) you can use is a lvl 15 Spear, best at lvl 20 ; because that's then you unlock the weapon's SBB and it gets a fairly strong HoT, by SArc's standards that is. Since you could get poisoned by Balamgram, a Spear with HoT is really quite useful along with it's pretty solid defense buff.

The next weapon you could possibly consider is the Twin Pistols, found in the 5th area of Vilanciel they really are very useful. With the Pistols, you get a BC Efficacy boost as well as a Spark Damage boost, and with how long filling a units BB gauge really takes, BC Efficacy is very much quite welcome.

LS spheres you should use, or consider are the Shining Stone, Noble Blood Gem, and/or the Lupine Mantle, I did it myself with a Lupine Mantle friend while using a Shining Stone myself. The Shining Stone boosts your max HP and Rec parameters by 20%, it's that simple. The Noble Blood Gem is the upgraded version of the Shining Stone and boosts your HP and Rec by 25% along with a 20% chance to heal you for 30% -60% of the damage you deal.

The Lupine Mantle is the sphere you can craft after defeating the Mystical Wolf in Vilanciel's other EX dungeon. The Lupine Mantle boosts all parameters by 25% and gives a probably boost to your BB gauge when attacked, and a chance to fill when normal attacking (no numbers given).

Well, this is the end of the guide, hope it helped!

        - W00DS

Edit: Link to my other guide for fighting the Mystical Wolf in Vilanciel's other EX dungeon