You can bring a Rider here, as this first wave isn't that hard (it's still a bigger threat than the first quest's first battle), but be sure that the Rider is well-protected or sustained. They'll need it in the next battle.
Chimeras are usually Berserkers and takes longer to charge up their NP blocks, but this time they're Assassins, meaning that they can unleash their NPs after 3 turns. If you cannot eliminate them quickly, bring a Caster.
The Vanguard is a Daemon type enemy. It possesses massive HP. Hopefully your Rider can accumulate NP for at least one NP strike.
Fergus has a skill to increase his own NP Gauge
When his HP drops to below 100,000, he will use a skill that increases his defense and grants 1-turn Evade.
Strategies & Recommended Servants
As stated, Riders are recommended early, at least until the 2nd battle is concluded. Ushiwakamaru has the potential to one-shot the daemon with her NP, but Georgios can withstand the demon longer with his tanking ability.
If by any chance Georgios isn't available, Leonidas can serve as an early tank. However, he will be less effective in the final battle as Fergus can drill through him.
Archers in general work well, but Euryale is incredibly effective against Fergus since she can charm him, her skill and NP allow her to deal extra damage against male enemies and she can delay his NP while charging her own. Try not to unleash her early, however.
The White Chimera should be taken out first before Fergus since it's a Berserker. Have your damage dealers go against it first before the man himself.
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For this quest, we forego Critical hitting into building up NP for spamming Noble Phantasm and drawing out the battle.
For the first wave, Georgios shouldn't start tanking so any Chimeras might attack Hans which is more resistant. Brynhild has a chance to destroy one Chimera in one hit, provided she has a Buster Chain
In the second wave, Georgios can start tanking while Hans spams his NP and keep the party sustained while all occasionally attacks and chips down the enemy HP. With proper defense buffs, Georgios can tank the demon's NP.
During the third wave, Brynhild should have a full NP to kill the Chimera in one hit, leaving only Fergus, who will target her until she dies. Until that time, Georgios is not to use his tanking skill. Meanwhile, Hans keeps sustaining as usual.
Brynhild gets replaced by Nobunaga, Georgios then activates his tank skill, so Nobunaga is kept healthy, until Georgios inevitably dies
In this third wave, the attention shifts into critical hits, since there's no one to decrease the critical strength anymore, and Nobunaga has innate power to manipulate critical gather rate and critical strength, making her more ideal on this.
Euryale replaces Georgios and she will be able to delay Fergus from using his NP with her skills and NP, while dealing good damage.
Fergus will eventually unleash his NP, in which both Nobunaga and Euryale can tank them. Give Hans evasion and the rest of the team lives through it, because Euryale's delaying will drop Fergus to below 100,000 HP, which triggers his skill activation instead of attacking. Thanks to Hans' NP and her class resistance, Euryale can withstand Fergus' attack later.
Leave the rest to Nobunaga to destroy Fergus and ending the battle.
This strategy is quite dependent on RNG thanks to the chance of Euryale missing her Charm on Fergus, or Hans' NP not activating the DEF Up buff on the right person. But it's doable.
Chaldea Combat Uniform
One: HP Restore to Dantes on the turn the mission was won (unnecessary precaution)
The first wave is used to build up NP for Shiki, Mary and Dantes
With this, Mary will be able to one shot the Vanguard at the second wave with NP Brave Chain, and her attack boosted by her 3rd skill
At the beginning of the 3rd wave, Mary gets swapped with EMIYA with Mystic Code, Shiki instant-kills the Chimera with 1st skill and NP, and then she gets killed by Fergus while EMIYA and Dantes continue to build up NP.
Euryale is too low-levelled so her job was to stun and delay Fergus with built up NP and Skill.
Once all three has their NP filled, strike with all their NP, and this will leave Fergus stunned and with small HP.
Command Spell is used to heal Dantes as a precaution in case Fergus survives the turn, but it turns out he dies in that turn.