I couldn't miss the chance to practice my drawing!
Like the raid event, the mission is a single battle against Shadow Bahamut. However Shadow Bahamut has increased strength and a staggering 6,000,000 HP, making it 50% larger than the Event's ELT level. The battle plays similarly to the previous fight but with significant differences. Bahamut is immune to Status Breaks except on its ATK stat which is meaningless as he largely attacks with Magic. Furthermore Bahamut begins charging his Megaflare before the party can take action, therefore ensuring the Dragon King's signature blast will occur immediately after the player's first turn. Given this version of the Boss' stats, a Megaflare left unchecked can wipe the party instantly.
As such the player is required to prepare. Materia that increases HP is a good idea, although attackers (Specially physical attackers who stand the best ground against Shadow Bahamut) should not forsake ATK boosts, for their HP is usually high and require mostly defensive measures. It is recommended that all attackers Guard during their first turn, reducing the damage of Megaflare by half, and that a healer with defensive buffs like Luka uses Deep Blue to increase the party's Defenses. Since Luka is a healer her SPR is expected to be high to survive, even without guarding, although she should be given HP boosts as her low HP can hinder her ability for survival. Y'shtola is another good option but given she uses Green Magic this is unwise if the player wants to achieve all Missions.
Following Megaflare the battle plays more or less normally with Shadow Bahamut using an array of elemental attacks that hit the whole party and normal physical attacks. The latter is not deadly but the former can pose problem so elemental protection is required. Cloud of Darkness' Omni-Veil or Marie's Love You All, will provide great defensive ability. Since Bahamut has pitiful defenses a well equipped offensive unit can chirp at his HP easily, specially the units from the event's banner. Others like Noctis or Fryevia are also helpful, the former can use Cover to buff the party with an HP/MP Regen, the latter can inflict major Ice Damage. Orlandeau is not completely foolproof as Shadow Bahamut has 100% resistance to Light so his Divine Retribution will be impaired.
If the player attempts to beat him with a five-man party then it is recommended they play defensively. 2 Healers and 1 Elemental Buffer like Cloud of Darkness, Marie, Minfilia or Cerius (this one can Dualcast but has limited elemental coverage) and 2 attackers. The player should use Companion for whatever unit they lack under this setup. Sakura is also helpful due to being able to reduce 20% of all damage done.
Shadow Bahamut will recast Megaflare after 40% of its HP is depleted and every 3 turns after. However there is a bug, which will cause Shadow Bahamut to not use Megaflare (even if he charges for it) if you knock its HP to the 40% threshold on turn multiples of 3 minus 1 (turn 2, 5, 8, 11, 14, ...). Shadow Bahamut cannot be one-shot killed as his HP will not decrease after he initially reaches the 40% threshold, but will take damage afterwards.
To defeat Bahamut with an Esper it is not necessary for the Esper to deal the killing hit. Overkill damage also counts for this. Also if the Esper is summoned prematurely and hits Bahamut before his HP reaches 0 but is used on a chain of attacks that kill Bahamut it will also count. Therefore it is recommended the player minds their damage output and calculates how much damage they can inflict, and before attacking Bahamut the player should summon the Esper (AND let the attack sequence to be visible) and attack immediately afterwards.