I couldn't miss the chance to practice my drawing!
The player should be prepared as Titan is a much more difficult challenge than Shadow Bahamut, due to his many quirks. Titan's attack contrary to any first impression are not Earth-elemental, instead they are all Non-Elemental so any elemental protection is useless. The battle against Titan has three phases.
Titan can attack up to 10 times per turn and will usually spam normal attacks, Rock Buster a single physical attack, Weight of the Land a single magic attack, Rock Throw which inflicts petrify on a single unit, and Tumult a physical attack that affects all the party. Also once every four turn he will use Landslide which will permanently remove one unit for the remainder of the battle.
Of all his attacks Tumult and Landslide are the most dangerous. The former if spammed too much, can still kill the party, so the Trial is partially, luck-based. Landslide can be prevented, but the player will have to be quick and be able to trigger Titan's next phase within the allotted time.
The first phase will conclude when Titan's HP is brought to 60% (3,200,000 damage) at which point he will cease to take damage (therefore he cannot be killed in one turn, regardless of preparation). Once this happens, Titan's Core will spawn and the turn ends. Titan will take no damage unless the Core is destroyed, which is the second phase of the battle. Titan will still attack but the Core will do nothing until the 5th turn, at which point it will use an extremely powerful version of Earthen Fury that will kill the party. This attack can be evaded, but it will spam it every turn after as well. The Core is not susceptible to Stat Breaks but Titan is, so the player should be careful to aim their debuffs at Titan and not the Core. The Core has 1,300,000 HP so if the player could stop the 1st phase down within 4 turns, they should be able to manage this damage-wise. However survival is still dependant on Titan's attacks as Tumult remains a looming threat. The player should still focus to destroy the Core on the Fourth Turn, doing so in less, will still allow Titan to use Landslide on the next phase which will be fatal.
When the Core is destroyed Titan will use Earthen Fury, although this is a significantly weaker version. This still can be damaging but not necessarily fatal. During the third phase, all of Titan's attacks are stronger and the battle becomes effectively a race to destroy Titan as quickly as possible. Only careful preparation will allow players to succeed here as the damage will eventually pile up.
Titan is a Stone enemy, so the player should employ Stone Killer to damage him the most. The Esper Golem carries this, so equipping it to attackers is a good idea. However the player should be mindful, because if Golem has Cover, the attacker risks using it to protect another unit which will cause him to take twice the damage from Tumults, likely resulting in death unless the unit has high evasion. The party should all be equipped with anti-petrify equipment. Gold Armlets, Safety Bit, and others are all recommended, Gold Armlets in particular are good due to providing MP so it can allow the player to meet the "No Items" criteria easier by forsaking the use of MP items.
To survive Titan's attacks the player should buff their DEF/SPR and debuff Titan's ATK/MAG. For both, values of 45% and above are greatly recommended, specially so for the debuffs, as otherwise they risk death. Buffing the party's offensive abilities is also essential to meet the four turns time criteria. Refia's Embolden is a good buff and she's an effective healer (however she will need Dualcast as otherwise she will not suffice). Ling is a great unit to use as her Daunting Step can reduce both ATK/MAG by 45%, and she also can use Invigorating Dance to restore MP if needed. Y'shtola can Dualcast on her own and has protective buffs, but she cannot bolster the player's ATK on her own. Sakura's Defensive Barrier is useful to keep the damage on check, but it alone won't suffice.
To damage Titan, it is recommended the player builds up Chains and uses a Chain Finisher to inflict the most damage. Chizuru, Orlandeau, Fryevia, are all useful for Chaining. Good finishers can include Noctis, Olive or Aileen, the latter has innate strengths against Stone enemies. They should all have Dual-Wield to maximize the damage. Once more the player should be careful to finish each phase on the Fourth turn. Before or after will not prevent Landslide.
On the third phase, the player should Evoke Golem. This will help them mitigate the damage and survive the turn along being able to set up and damage Titan, giving them more ample room to maneuver on this damage race. For this phase extreme damaging abilities are required as the player will likely see their units die slowly. Buffs and Debuffs remain important but they will not be sufficient without the ability the defeat Titan quickly.
A good strategy to use here is to exploit Noctis' Arminger which can provide massive buffs to the entire party for two turns. However an Arminger no less than at level 20 and above is absolutely essential, in order to gain a buff of 70% at least, otherwise it will not suffice. In order to exploit Arminger the player should use Ling's Entrust to fill Noctis' LB bar. Ling's bar fills quick, so she can shift between Daunting Step and Entrust. Chains should ensure sufficient crystals are dropped to fill her bar. In order to reinforce this strategy counters like Snow and Chizuru are fairly useful. Snow has great counter abilities and serves as a good tank, while Chizuru is a chainer and her counters can provide additional crystals.
Even with a high level Arminger the player is not guaranteed to succeed as Titan's attacks remain feral. This third phase ultimately tests the player's ability to deal large amounts of damage quickly, while being able to survive long enough to do so, as Titan will have 4,800,000 HP, things will be more difficult than taking down a single Titan in ELT.
Given the four turn management and chaining are essential to win the battle, the player should practice their timing and damage output in ELT. There Titan has 4,000,000 HP and his defensive stats are the same as in the trial, so if the player can take ELT Titan down to 25% HP within the four time limit, they should succeed in the Trial. Once more, the player should aim to beat a phase ON the fourth turn, as either before or after will not prevent Landslide.