Here's a step by step method to clear the Maw of Malice battle with all missions.

Note that the attack pattern of the boss has some slight RNG to it. Sometimes he won't cooperate with this attack pattern and uses things like 5 AoE's in a turn and kills someone. If something goes wrong just retreat and try again. It's only 5 energy.

This boss is harder to make an exact script for, so you may need to adjust on the fly, but for the most part, this should be repeatable:

Pre-fight prep: Equip White Fang, Blue Fang, Holy Torch, Elixirs in your battle item chest. (Note: Other elemental damage items work too if you don't have story access to fangs yet)

Turn 1:

• Lucas: Forced Engagement
• Lenna: Mystical Telluric Waters Dance of Glimmering Water
• Fid: Water Fight Ultimate Siesta
• Rain: (Item) Blue Fang
• Xon: (Item) White Fang

This sets up provoke, fire resist, general mit, break immunity, LB fill, breaks, and gets the ice thunder mission completed. Your team should survive turn one. With horrible RNG on the bosses attacks, you may lose Rain. If that happens, start over.

Turn 2:

• Lenna: Princess's Devotion Heavenly Healing Waters
• Fid: Lovely Water Beach Attack
• Lucas: Ethereal Core Elemental Cover
• Rain: Extra Saber Complete Awakening
• Xon: (Reflector) Critical Mirror (on Rain) Elemental Mirror (on Lucas) Survival Mirror (on Lucas)

More setup. This queue's a heal for next turn, imbues us with water, imperils the boss to water, applies the rest of the immunity buffs, gives us physical mit, fire and dark resist, fills Rain's LB and buffs his ATK by 250%, and lets Xon copy all those juicy buffs to himself for both the self buff, and to prepare to share later. Survival should be fine now.

Turn 3:

Lenna's queued heal tops everyone up. Xon "should" have his LB ready from drops and the LB fill buff, but I'll assume your RNG was bad and Xon didn't fill. If he did, you can use Lenna to do other support stuff this round.

• Lenna: Entrust Xon (or free turn if Xon filled from drops)
• Rain: Limit Burst (chain with Xon)
• Xon: Limit Burst (chain with Rain)
• Lucas: Mythical Sanctuary
• Fid: Beach House Break

The chained LB's push the boss to 80%, where he HP locks. Fid uses Beach House Break to help re-fill Xon's LB for later, and to help fill Lucas (and Lenna if she entrusted). Mythical Sanctuary finally gives us Magic Cover. The boss will do some more nukes and buffs on his turn.

Turn 4:

• Rain: (Triple) Soul Blood Energy Wall Rise Aldore Leader
• Lenna: (Item) Holy Torch on boss
• Lucas: (Magnus) Epitome of Defense
• Fid: Limit Burst
• Xon: (Reflector) Critical Mirror (on Rain) Elemental Mirror (on Lucas) Projected Mirror

Lenna dispels with an item while Fid re-breaks. Rain powers up his LB with his good burst cooldown while Lucas uses his magnus buff, which is normally only one turn duration. Xon now copies Rain's LB boost buff and Lucas's magnus, then he shares those nice buffs with the whole party for a four turn duration, which is long enough to finish the fight. This also refreshes Re-Raise on everyone due to the earlier copy.

Turn 5:

This step is slightly subject to RNG. If the boss buffs his defenses it's harder. If he skips buffing this turn, you've got this. If he did buff, you could holy torch again with Lenna and re-break/imperil with Fid before attacking.

• Lucas: Limit Burst
• Fid: Lovely Water Beach Attack
• Lenna: (Free Turn) Use whatever you want. Heal the team if they're damaged.
• Rain: Limit Burst (chain with Xon)
• Xon: Limit Burst (chain with Rain)

With breaks, imperils, and Rain's copied soulblood, you should chunk the boss all the way to the 5% hp lock on this turn. With Lucas's copied magnus still active, and now his LB buffs finally online, survival shouldn't be an issue as the boss does his 5% threshold stuff.

Turn 6:

It's possible someone dies here, but Re-Raise should still be up because it was refreshed when Xon shared buffs a few turns ago. You also may have zero mana due to drains at this point, but it doesn't matter.

• Lenna: Genuine Generosity
• Rain: Limit Burst (chain with Xon)
• Xon: Limit Burst (chain with Rain)
• Fid: (Free)
• Lucas: (Free)

Lenna's Genuine Generosity costs 0 mana to cast, which AoE fills everyone's LB. Then just chain Rain Xon LB again to deal the last 5%. Victory. (The boss does lock at 1% hp for some reason before dying on his own turn. Don't panic!)

Final Words

Here's a video of the above in action: https://www.youtube.com/watch?v=e8uI3P-SFng

Hope this has helped!

Reminder

There's an element of RNG to his attacks! This run may not go exactly as shown, but you should be able to repeat this within 1-4 attempts.