The Order's Training Facility and Armory are located in the Castle.
Walkthrough[edit]
Fifth mission: Kill the Programmer[edit]
You start in the northeast of the map (A). Go through the door to your right and down the stairs to the Armory. (The room to your left at the top of this staircase contains only two Med Patches and some enemies, who for some reason ignore you; the door to your right can't be opened from this side.) Grab all you can, then back up the stairs and down the passage to your right. Just before it turns you will find the second of the False Programmers (B).
Continue (past the Armory and beneath the ceiling turret you took out a few moments ago) to the Training Facility. Enter, and cross the moving platforms (past a door you can't directly open; if you're careful not to fall in the sludge, or you minimise your time in it if you do, you can get through without using an Environmental Suit) to the button at the end (C). I'll give you one guess what this one does... Yep, after pressing the button in the south (your right as you face it) alcove (you don't need to press the other button as its action was already performed by the first one), go back and enter the now-open door (D).
Press the button in front of you to reveal an ammo box (and a Crusader); then the button on the lintel into the next room to raise a stairway. At the top, press the buttons to open the two teleporters in the other room, then go through them (they each go to the opposite corner) and press those two buttons to open the way to the next room, and go through. You will be teleported to an area in the northwest of the map (E). Turn left (go south) and around to a locked door (I; it is actually a set of three locked doors), then left (northwest) and go around the block (in either direction) to a lift (F). Ride it up and press the button; you will probably see the first of those three doors open in the distance. Unfortunately, you have also opened several holes in the floor which you will have to take running leaps over.
Drop down and head back to (E) (left, left, right, left, left) and continue into the corridor you went down before; there will be one of those gaps to jump. A bit further on you will come to a newly-opened staircase; go up it and press the second button (G) (you may see another door opening), then retrace your steps to (E) and go across to the lift at the other side of the room (H). Go around and press the final button, then go to and through the doorway (I). Press the button, and you will be congratulated on completing the course. You will also get an automatic stamina and accuracy increase of 10 points each. Now all that remains is to go through the door, restock at the Armory if need be, and head back to the Castle.