2.arousal/border alliance
Check the bulletin board.
Talk to Rin on the Roof.
Go to 1F for a conversation with your Servant.
Talk to Sakura in the Nurse's Office to obtain your weekly item.
Check the Commissary for new items. There are always new items added at the beginning of each week.
Go to the Arena entrance for an event.
Enter Arena 1F.
The arena is poisoned—your HP and MP will gradually drop as you run.
You need to reach a tree a little way into the arena.
You will spot Dan on the way there. Choose to stay hidden. The other option is a one-way ticket to a Dead End. Yes, you can now reach Game Over from decision prompts.
Now continue to the tree and destroy it.
You are now free to continue through the dungeon.
Be sure to pick up the 1st Trigger on your way through.
If you have Saber, go to your Private Room for an important conversation. Choose the 3rd option.
Talk to the marked girl in front of the 2-A classroom.
Head toward the 2F stairs and talk to Rani.
Talk to Taiga in the 1F lobby to get the quest to get a persimmon.
Enter Arena 1F.
You need to pick up 3 items related to Dan's Servant while here.
The first is at the location where you destroyed the yew tree.
The second is in the southwest corner of the large middle area. Note the Box of Persimmon is also in this room, so be sure to pick it up while you're here.
The third is at the dead end you reach after taking either the 2nd or 3rd west hallway after heading north from the central room.
If you need to go to the Chapel or Commissary, warp there via the square button. Definitely do not go on foot via 1F. With that out of the way...
Go to 1F for an event. Choose to escape to the arena.
Progress through the arena normally toward the large central area for an event. You get Matrix Level 1.
Hurry to the north exit.
You get Matrix Level 2 after an automatic event.
If you have Archer, go to your Private Room for an important conversation. Choose the 3rd option.
You can go to the Library and read the marked bookshelf for more information on the Yew Bow if you want.
Talk to Taiga in the 1F lobby to give her the Box of Persimmon and accept a quest to bring her someone's glasses.
Enter Arena 2F.
You'll need to hit a switch at the far east to open the door to reach the 2nd Trigger. Once the door is open, you can find it at the end of a southbound hallway directly to the south of the northbound hallway leading to the exit.
Be sure to pick up the Demonic Eye Blocker from the northwest while you're here.
[Note: Demonic Eye Blocker is typically translated as Mystic Eye Killer. The Type-Moon faithful will know why this item is the "glasses" Taiga wanted you to find. The rest of the game makes it pretty obvious that the translator for the official English version of this game had never touched anything related to Type-Moon before and put no effort into research to make up for it.]
Talk to Rani on 3F.
Enter Arena 2F.
Go to the room right before the north exit to meet Dan and fight his Servant. He uses Poison Arrow for the 2nd action of the 2nd turn and Wall of Thorns for the 6th action of the 3rd turn. Both are attack Skills. You get Matrix Level 3 after the battle.
If you have Caster, go to your Private Room for an important conversation. Choose option 3, then 3, then 1.
You can check the Library for more information about yesterday's encounter if you want.
Give the Demonic Eye Blocker to Taiga in the 1F lobby.
Enter Arena 2F and grind until you're satisfied that you're ready for the boss.
Go to your Private Room and organize your information to get Matrix Level E.
I would highly recommend that you equip the Exorcist Blade and/or buy several Remedy.
When you're finished preparing, talk to Kotomine in the 1F lobby.
Archer always uses Guard for his first action every single turn. That means you can either use Break or freely use buff Skills for your first action.
He uses Poison Shot on the 2nd action of every other turn, starting with the 2nd turn. That means he uses it on turns 2, 4, 6, and so on. This Skill has a high chance of causing poison. It's best if you use Hack to stop him from using it entirely.
If you are poisoned at the end of a turn, Archer will always use his Noble Phantasm for the 2nd action of his next turn. If you use a Remedy to cure your poison quickly, you won't have to worry about his Noble Phantasm. It has no effect on you whatsoever if you're not poisoned at the time when he uses it.
He sometimes uses Wall of Thorns to attack you for either the 3rd or 6th action. It doesn't do much damage, so you can just Guard it if you don't want to use Hack. Keep in mind that you can't heal and use Hack in the same round.
At low health, he rarely uses a Skill called Faceless King. It is a buff that causes him to automatically win every contest of basic actions until it wears off, even if you chose the winning move. If he uses it, use attack Skills instead.