4.MONSTROSITY/telesthetic longing
4.immortality/howl of the blue moon
From this point forward, the story splits into two versions: the Rin Route and the Rani Route. Cutscenes aside, the actions you need to perform are practically the same. Therefore, making two separate walkthroughs would be excessive, so I won't be doing it. As minimal as it is, anything specific to the Rin Route will be highlighted in red, while the Rani Route will be highlighted in blue.
Check the bulletin board.
If you have Saber, go to your Private Room for an important conversation.
Go to the Library for an event with Leo.
You can leave and reenter the Library and talk to Leo again if you want to learn more about the Holy Grail.
Talk to Rin/Rani in the Nurse's Office.
Talk to Sakura to get your weekly item.
Go to the 1F foyer for an event with Rani/Rin.
Enter Arena 1F.
The Trigger is in the center of the map. The pathway to it extends south from the middle of the passage along the north of the map. Follow that hallway south until you come close to a shiny point to trigger an event. When the enemy Master appears, choose to observe them.
You can't continue past this point today, so explore the rest of the dungeon. Be sure to pick up the Shockwave-2nd Strike item next to the exit in the northwest. This Formal Wear gets increasingly valuable as the game progresses, so hold onto it.
Talk to Rani(3F)/Rin(Roof).
Go to the Nurse's Office for an event with Rin/Rani.
Enter the Arena 1F.
You can collect the Trigger today.
A new rare enemy type called a Nephilim has spawned on the path leading to the exit in the northwest. These enemies are more formidable than regular enemies and give far more EXP, but they do not respawn once you've killed them. Also, if you're using Caster, defeating 5 of them as you progress through the game will upgrade one of her Skills. There are more than 5 in the game, so it isn't the end of the world if you miss one—it only pushes back when you can start using that upgrade.
Talk to Taiga on 1F and accept the quest to get the Crab Omelet.
Go to the Nurse's Office for an event with Rin/Rani.
Go to the Arena Entrance for an event. You get Matrix Level 1.
Enter Arena 1F.
Be sure to grab the Crab Omelet from the east side.
Give the Crab Omelet to Taiga on 1F and accept another quest.
Talk to the marked boy in the schoolyard.
Go to the Nurse's Office for an event with Rin/Rani.
If you are playing a female character with Archer, go to your Private Room for an important conversation. Select the only option and then either option 1 or 2. Both get the same result.
Go to the 1F foyer for an event with Kotomine.
Enter Arena 2F.
The goal for this event is to defeat more Carnivores than the enemy Master. They are represented on the map by the larger-than-normal red squares. This is easy to pull off—just run and take out as many as you can. I would recommend heading toward the northern half of the map for easier pickings. Make sure you don't run into the enemy Master in the process. After all of the Carnivores are dead, the enemy Master will leave.
Explore the dungeon at your leisure. Don't forget to pick up the Shark's Fin from the entrance to the northern section and the 2nd Trigger from the eastern offshoot of that area.
If you have Caster, go to your Private Room for an important conversation. Choose option 2, then 1.
Go to the schoolyard and give the Shark's Fin to the boy.
Go to the Nurse's Office for an event with Rin/Rani.
Enter Arena 2F.
The Carnivore hunting event from yesterday is repeated.
After that's done, the enemy Master will challenge you to a fight. You get Matrix Level 2.
If you have Archer, go to your Private Room for an important conversation.
Talk to Taiga on 1F.
Go to the Nurse's Office for an event with Rin/Rani.
Talk to Touko in the Chapel.
Go to the Arena entrance for an event with Kotomine. If you won the hunting event, you get Matrix Level 3.
Enter Arena 2F.
A Nephilim has spawned today near the exit. It's the same version as before, so it should be easier to take down now that you've gained some levels.
Grind until you're satisfied. This should be your first truly challenging boss fight, so whatever level of readiness you think you need, add some more to it.
Go to your Private Room and organize your information to get Matrix Level E.
When you're finished preparing, talk to Kotomine on 1F.
Lancer starts the fight by using a buff to strengthen his Guard counterattack. He always uses it for his first action every 3 turns, so turns 1, 4, 7, etc. He doesn't really Guard that often—except for occasionally when he does nothing BUT Guard for an entire turn—so it's not a huge deal. However, when Lancer guards for a whole round, his Master can use a code cast that seals your Break action.
Lancer uses Ceremonial Purge for his 5th action every 3 turns. This Skill does damage equal to how much you damage him. Ideally, you should prevent him from using it.
Once you get his health low enough, Lancer will start using his Noble Phantasm. He typically starts using it the 2nd turn after the indicator appears. It's easy to tell when Lancer's about to use it. He and Ronnie will converse in an ominous tone before that turn. He always uses it for his 6th action. However, it can't be blocked with Guard. You can defend against it with Archer's 7 Rings of Heaven or Caster's Mantra: Aphotic Cave. Or you can just prevent it with Hack.
Boss Strategy: BerserkerThis fight is pretty straightforward. That's not to say it's easy, quite the opposite. There's just no fancy cure-all strategy for it is all, so just fight.
Berserker only uses her Noble Phantasm for her 6th move. Before she uses it, her Master will yell out, "Waga kamiyo! Waga inori yo! Junbi wa yoroshī ka?" so be sure to Hack or Guard it somehow because it hits hard. She always uses it for the 6th action of the first turn.
When the moon icon is present, she has a chance of using Gnaden Sturz, which does substantial damage and paralyzes. You definitely do not want to get hit by this. Stop it with Hack if you have a Master action available. Otherwise, use a defense Skill if you have one, Guard if you're Saber. She uses it on the 6th action, so I would recommend you assume she's going to use it if you see the moon icon but don't see her 6th action. Unless, of course, the enemy Master has announced a Noble Phantasm turn... which you should be reacting the same way for anyway. Without the moon icon, she only uses buff Skills and only for her 4th action.
Berserker Waits a lot, which gives you a substantial advantage, considering how high her attack power is. Her actions do not have much of a pattern to them—seriously, some of them are literally determined by pure RNG right as the action comes up. Remember that you can always use an attack Skill for any move you're not sure about. That will cancel any opponent attacks that are not Skills themselves. Just keep in mind that it isn't easy to recover your Servant's MP—impossible at this point if you're not using Caster. Make sure you bring plenty of recovery items or equip a healing Formal Wear.