hide in cells and wait for guards to pass. that's the easy part.

next you'll get to a section with two branching paths. you can either go down and stand on the stairs, throw a bottle at the fire alarm bell above you, then jump up again when the guard's gone to check it out. or you can jump over him and slice upwards to ensure you land right on the door (and just outside sight). either way you simply proceed and hide on the second staircase as you wait for next guard to pass on his own, after which you can move to the next room.

next go into tv room to watch the guard pass on the screen. simple.

now this is the hard part. outside, walk as far as you can and then wait for first guard to almost see you, then slowmo jump and slice diagonally for hight (mid air). let go off the movement before you land (if you have auto roll turned on) then duck under tables.
keep about a two table distance to guards and proceed to third table, wait for him to almost see you then do the same jump trick again, you should have enough time to get to the punching bag, duck there and then wait.
proceed and duck under the smaller dumbells as you move up. then either wait and do the jumping trick to land well behind the final guard there or go into the open and do it a little closer. don't try to hide at the stand. the jump trick gets you over basically every guard.

theres no need to do the fancy jump thing in the courtyard. you can also run without sneaking as long as you're about a third of your screen away from any guards, which helps you get farther faster. overall the same strategy of ducking out of sight that you used in the first room will help you here.- courtesy of a hoe meth yoda