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1: When you enter the Arcology building, you'll begin in the Maintenance level, just below Arcology 107 and it won't be on your map that you find if you go straight from the elevator and read the datacube under the power box. If you use your multitools on the power box, you can climb through the opening and enter a semi-secret room with energy cell and ammo clip if interested. Otherwise, ignore the passage to the Nanoformer Station and head up the ramp to Arcology 107. It will be a U-turn from the elevator passage.
2: When you get up to 107, you'll notice a couple templars at the recruiting station to the northwest. Talk to the one in the chair, and use any line you wish. Now head east to Peequod's Coffee Shop and speak with its manager. Like Queequeg's in Medina, he'll offer you something in return for getting the NG manager to agree to sponser Peequod's; in this case, it's a Biomod Canister, a better deal in my opinion than the weapon mods that Queequeg's was offering. In any case, in the corner of the same room, talk with NG for a new quest to find any information on corrupt officials.
3: After NG, head west and then into the Tarsus Academy section. Before you enter, notice the trash can on the west wall "hiding" a grate. Climb in and use your Spy Drone on the lasers ahead. Crawl through to the open room, ignore the shaft on your right, and continue through the shaft straight ahead. Soon you'll come to the templars you've already talked to. They'll be in conversation, and if you stop to listen, you'll complete your goal of spying on the templars for Leo. Now enter the Tarsus Academy.
4: Approach the Sandra Bullock-esque receptionist and you'll get another objective from Donna Morgan to find the missing students. Talk to the receptionist and enter the academy. At the first intersection, you'll notice a group of two kids on the right. Talk to them to find out some info on the missing students. Then turn around and head to the lecture hall on the left. Talk with the students and teacher, exit the room and take a left until you get to the Nanotech lab with guard standing outside.
5: Talk to the guard to get another small quest, that of killing the red greasels inside. If you got the secret Red Greasel Gun from before, it's a good choice and you can add an increased damage weapon mod to make it more effective. Simply walk in and use the tables for cover, and fire away. When they're dead, go to the guard for your reward and then back inside. Against a back wall, there's a cabinet with a normal BIOMOD CANISTER and a couple items in other cabinets. Enter the vent shaft on the bottom of the back wall and you'll pop out in a hidden room to find the missing students!
6: Talk with Eeva Nassif to learn where the headmaster's secret office is. You can either drop down the cubby hole and walk along the maintenance shaft with harmful steam spouts (but a multitool!), or take the easier route on top through the vent, though you'll have to deal with two spiderbots, and no multitool. I prefer going down, taking the multitool on the ground not far in, and coming back up through the vent. Take the vent shaft all the way down past all the ladders and spiderbots until you come to a dead end.
7: Open the grate to find a camera scanning the back wall of this, the headmaster's secret office, and a turret nearby. Use your Spy Drone or EMP alt-fire from the Mag Rail to take out the camera and drop down into the room. View the holocomm to get the keycode for ApostleCorp and read the datacube to incriminate the headmaster. Inside the safe is a fragmentory weapon mod, so use your multitools unless you can hack. Open the door in the room to find a repairbot and a ladder leading down.
8: Purely optional, but if you want a load of equipment, descend the ladder and defeat three unaware Templar Paladins below with your Spy Drone or other method, and then clean the room of stuff you need. Head back up and exit the headmaster's room through the circular stairwell leading up. Open the secret door at the end to arrive in Silas Archer's Office, shown on the map. Take a left and talk with the student at the detention desk, then read the datacube on the ground to the right of the desk for the Tarsus Admissions Login you'll need shortly.
9: Talk to Silas Archer (the headmaster) under the window, but I'd advise not confronting him about what you know because you'll get to let the authorities take him sometime after you tell NG. Of course, if you want to kill him, it's your prerogative. Exit the office to the left, and follow the corridor to the receptionist's office. Use your newly found admissions login on the computer at back to approve Ameer's admission, though your monetary reward, if you go back to the Infirmary in the Church is 5 credits... almost enough for a gumball.
10: Leave Tarsus back to Arcology 107 and report Archer's corruption to NG, who will direct you to the SSC Guard Station in 108 for your disbusement. Behind the coffee shop is the ramp to level 108, so take it and bypas the Order Church elevator on the way. When you're up, head all the way right to the SSC Guard Station and speak with the guard. Tell him you have a crime to report, and collect your 300 credits. Behind him and the yellow beams is a room with a Black Market BIOMOD CANISTER. If you want it, you can send your Spy Drone to disable the beams and camera behind you in one shot. Exit the guard station when finished and take the nearest door to your left into the Arcology Air Terminals.