Take extra care to not be seen by the guards positioned by the windows when you’re moving across–wait for them to move away before proceeding. Climb over the broken section of the balcony ledge and start sliding across to the next one. Afterwards, head out and take out the guard positioned at the balcony.
Move in here and take them out (the further guard will likely not notice you enter). There are two guards in conversation in the nearby side room. Take out the first guard when he begins to walk away from your starting point. Stealth is a key factor in this mission, so keep that in mind as you begin.
