Combatants Remaining: 128
Have your starting conversations with your Servant and with Sakura.
The commissary (downstairs from 1F) is open now, so you might want to stop by and buy some healing items.
Go to the Roof and talk to Rin.
Talk to the marked girl in your class.
Go to 3F and talk to Rani.
Go to the Roof and talk to Rin.
Go to 1F and talk to Kotomine. You can now magically access your "Private Room" at 2-B. You can go there anytime to speak with your Servant in private.
Talk to Taiga and accept her request to find her Kendo Sword.
Go to the Arena entrance at the famous spot at the left end of the 1F left hall. Enter Arena 1F.
The color coding of the maps should be obvious enough, so I will not be repeating them every single time.First Chimeric Lunar Sea 1F
Yellow are item folders.
Green are health fountains in easy mode.
Blue is the entrance and dark green is the exit.
Just train in here for a while to gain a couple levels. Your Servant won't let you approach the bee-type enemy blocking your path forward. Leave the Arena to end your day.
Go check the bulletin board.
Talk to Kotomine in front of the stairs on 2F to learn how the Cipher Keys work.
Go to 1F and talk to Shinji.
Talk to Sakura in the Nurse's Office to obtain your weekly item.
Enter the Arena 1F.
Go forward and you will run into Shinji at the point you couldn't go through yesterday.
You will fight his Servant. Your goal is just to survive for 3 turns (pretty easy in this case). Note for future reference this is always the goal for Servant battles in the Arena mid-week. Note she uses her attack Skill only on the 3rd turn. You get Matrix Level 1 from this encounter.
Continue on through the dungeon and be sure to collect the 1st Trigger and Kendo Sword.
Leave when you're done to end your day.
Head toward the hall in front of the Library to see an event. You get Matrix Level 2 (note: Shinji is the king of idiots).
You can check the marked shelf at the Library if you want to learn more. Speak to the marked girl in the back.
Go train in the Arena until you're satisfied and then end your day.
Shinji's up to something (probably something ridiculously stupid as usual). You need to investigate.
Talk to Rin in front of the 2F stairs.
Head to the Library and check the marked bookshelf.
Talk to Shinji for a bit so he can for some reason explain his master plan to you (well, that was easy).
Go to 1F and talk to Kotomine.
The Chapel is now open. You can go there from now on to assign any stat points you've earned through leveling up. I would highly recommend you go there right now to spend all the points you've surely built up by this point. I won't be reminding you to return to the Chapel from here on. Just recognize when it's needed and do it.
Leave the Chapel for an event with Shinji.
Talk to Taiga to give her the Kendo Sword and accept her quest to get her fruit.
Go to your Private Room for an important conversation with your Servant. For Saber or Archer, pick the 3rd choice. For Caster, pick the 1st choice.
Enter the Arena 2F.
First Chimeric Lunar Sea 2F
Purple is a switch and a red line is a door opened by a switch.
There is a switch to the left of the sealed door that opens it. They won't usually be this close by in the future.
After the long path running from West to East along the North side of the map, take the lower path at the fork. Your Servant will point out that there is a hidden passage, and that Shinji is just the type to hide his stuff in an obvious place like that (although you've passed 2 of those already, so one has to wonder why your Servant didn't say anything then).
Shinji will rush toward your location. You have to survive 3 rounds again (even easier this time). You get Matrix Level 3.
Continue on through the dungeon, and be sure to grab the Tangerine on the way to the exit and the 2nd Trigger right before you reach the exit. Definitely grab the Exorcist Blade close by as well, as it's easily one of the most useful Formal Wears in the game.
Leave when you're done.
Go to the Arena entrance for an event.
Check the door to the Nurse's Office.
Note you can now use the square button to fast travel within the school.
Go to the hall in front of the Library on 2F for an event with Rin and Shinji. You can check the marked bookshelf at the Library for more info on yesterday's encounter if you want.
Check Shinji's desk in 2-A.
Go to the Arena 2F and train until you're satisfied.
Talk to Taiga to give her the Tangerine.
Go to the Arena entrance to see an event.
Enter Arena 2F.
The goal here is to grab more Pirate Booty than Shinji. Every one he gets will strengthen his Servant a bit.
It is normally impossible to get the first 2. If you can catch Shinji and force him into a fight, he will leave the Arena, allowing you to get the rest for yourself. This should be your immediate goal. Chase after him (note time freezes for him if you get into a battle with a normal enemy). After he picks up his 2nd Pirate Booty conveniently placed at a dead end, you can easily cut him off in front of the place where you picked up that book the other day. Do so.
[Note: If you're playing a New Game +, you can just use Enhancement Spike to increase your speed and catch up to him before he even reaches the first one. This way you can collect all 5.]
Once Shinji has left, collect the remaining treasure at your leisure. Train until you're satisfied (this is your last chance this week), then leave.
Go to your Private Room and organize your information. It lets you retry if you make a wrong choice, and the questions are easy anyway, so have at it. After you've answered everything correctly, you get Matrix Level E.
You should assign any unused points at the Chapel and buy recovery items at the Commissary. You can sell the Pirate Booty for 2000 PPT each.
I would recommend equipping the Exorcist Blade.
When you're finished preparing, talk to Kotomine in front of the elevator on 1F.
Boss Strategy: Rider
Easy fight. She will use a buff on her first turn of any round where it is not already active and her Noble Phantasm isn't available, so, if you use Hack and keep her from using it, she will keep repeatedly trying to use it the first turn of every round, making her actions that much more predictable. If she ever gets the chance to use it, she will use her only attack Skill only on the 3rd turn. Anyway, there is nothing she does that you really need to worry about short of her Noble Phantasm which she uses when her health is below 30%, and it should tell you when it's coming (and she always uses it on the 6th turn). You can use a well-timed Hack (assuming you equipped the Exorcist Blade) to prevent her from using it entirely.