Hardest Battle in Shinjuku?

I really didn't think any of them were particularly challenging. Probably the second to last fight. Ended up being a faceoff against Moriarty and Cú during which I sweated at least a little.

First battle where the dog was an Avenger. Was glad to finally put it down after losing so much.

The Battle against Moriarty and Bael was hard, I agree with that.
But for me, the hardest was the last against Lobo, iirc.
The thing is, I did Shinjuku with Evil Servants only as a challenge. Well, nearly only. I always had Mash on the last place to save cost).
Anyways, at the moment, my strongest evil Berserker is Kiyohime Lv. 90. Though she's already bond 10, so I didn't even want to use her at all.
My second Berserker would have been Cu... Level 50 or so. I only got him recently, so didn't manage to level him that much (also missing some mats).

Tl;dr I fought Lobo (Avenger) with Jalter, Kiyo Lancer, Salter, Salter Support, Liz, Mash.
It was a tremendous defeat. Thinking back, it probably would have been wiser to put Mash on the front line.

For me it was the evade-spamming lobo. Probably was only hard because he critted down Euryale on the first turn so I had to use Robin instead. 🙃

The Enigma and Demon Pillar fights would have been hard if Robin’s poison had missed. But it didn’t, so I was able to burst both of them down pretty quickly.

Hmm, that Emiya Alter fight caught me by surprise. I brought Santa Lily instead of an ST lancer. That was probably the toughest for me.

I'd have to agree with those saying that the battle with Avenger Lobo and Moriarty & Bael were the hardest.

Against Moriarty & Bael I had a lot of trouble trying to figure out how to get around Bael's NP with the Nul Buff before damage. I ended up just focusing Bael down first using Herc and swapping in Leonidas to taunt the NP. Hardest part was probably lining up Bael's NP, his break bar, Herc's NP and Leonidas's manaburst. After Bael was down I just sort of raced to kill Moriarity between EMIYA Alter's NP and my Enkidu's NP.

Battle with Avenger Lobo. Because of the first turn evade spam. It ruined my Buster Gramps critical hit combos with double Merlin. Why I used Gramps? Because my only good berserker is Hercules and Lobo would have crushed him even with Double Merlin healing him.

Moriarty and bael for me too. I got rid of bael pretty quick but had trouble protecting myself from Moriarty's np spamming. In the end I was down to cu and herc with under 1000 health each and no evades or guts left and Moriarty's bar was full. Ended up using seals to restore health for each since I wasn't clairvoyant enough to guess he would choose cu over herc. Then one final buster brave chain from herc finished Moriarty.

The fight against Bael and Moriarty
I only beated ot thanks to Merlin and my trusty friend Asterios. I lost about 3 times before trying it woth an Asterios+Mash+Merlin comp and it took me 3 attempts but i won without losing more than 1k HP in the whole fight

I completed Shinjuku with Evil servants only and borrowing a support Merlin, pretty much the servants I used were:
Liz Lancer, Liz Caster, Ibaraki, Sanson, Teach, Salter, Atalante, Li Shuwen and Lu Bu, and the hardest challenge I had was the fight againt Hessian Lobo as Avenger. Both of them were difficult but I'd say the first one hurt the most to complete. It took me several tries and in the end I used CS.
I want to mention the last battle with Moriarty and Bael. Honestly it wasn't exactly hard, but it took me 2 tries to complete, mostly because it was a little tricky having an Archer with 3 bars to charge and a Demon God Pilar with AOE and effects I didn't know about.
Overall the singularity wasn't the toughest, but it offered good first taste of what's to come.

Hardest Battle? King Lear.... He kicked my frontline to death in 2 turn... 1st turn 3 times crit buff... Second turn kick everyone to hell...

Hardest Boss fight - Lobo in rider form 2nd fight I think... Since it's hard to have caster support in this battle it take longer to finish this fight.

Moriarty and Bael. Moriarty was no big deal against my Tamalancer, but Bael in particular got on my nerves with his ridiculous defense that made no sense in damage calculation. He was a sky attribute, and yet the damage dealt from my best mankind servants were not any different from the damage my best earth servants could inflict. Its like this god pillar was equipped with damage cut or something. Also, the crit damage and buff removals made all my defense and healing maneuvers useless. Why must goetia and his remains always torment my progression like this?

From all the bosses: The Avenger battle in chapter 13 (with def/attack down effects) was SOMEHOW the hardest boss battle. Was probably due to a combination of losing main DPS within first 10 turns AND running a mismatched all-evil team. Once I adjusted it somewhat, the boss went down on 2nd try.
To my great surprise, all 3 Moriarty battles seemed scarier on paper than in practice :S. Herc had to carry the team as a last one standing in 17-1, but the other 2 fights were like..."I was expecting more of a challenge" :S

From regular battles: 3 waves of of King Lears was by far the hardest battle.