Objective 1: Escape From Your Cell
Once the mission starts crouch and sneak behind the guard outside your cell and break his neck.
Objective 2: Get Your Map Computer And Lockpicks Back
Head to the place where your map computer and lockpicks are. There is a guard ahead and a camera at the top of the stairs. Wait for the camera to rotate and sneak behind the guard then break his neck. Get your things and head back.
Objective 3: Locate Priboi In Main Prison Building
Open the room just across, and climb up the stairs. There's also a security camera here so peek first before heading to Priboi's room. After you checked Priboi's cell, head to the room near the stairs to pick your SOCOM. Then get down and go back to the place where you got your lockpics/map.
Objective 4: Get To The Security Control Building And Hack The Terminal...
Shoot the camera on top of the stairs, and head outside. Hide behind the crates and you'll see an opening on the fence. Head behind the second crates, sneak past the guard/s and enter the nearby hut. There's a ladder here going down the sewers. There are four guards here which you can kill w/o them noticing you. Find your way on the other end of the tunnel and climb up. If your fast on doing the previous objectives you'll enter this area without guards patrolling outside the hut. Climb the watch tower and kill the guard atop. Get the sniper rifle (YOU'LL NEED THAT SAME RIFLE UNTIL MISSION 11 SO DON'T DROP IT) and slide down the wire. After that move around to the walls and into the security control building. Sneak past the camera outside the building and get inside.
Objective 5: Open Gates To The Inner And Outer Yards And The Main Gates
Head to objective 5 building and kill the guards inside using your SOCOM. Climb up the roof and kill the sniper. Pick up the rifles and from here shoot all guards that you can see. Just avoid any guard running to the alarm button. Once your done showing off your sniping skills, head back down and press the buttons to the inner,outer yard and main gates.
Objective 6: Take Down The 2 Guards Covering The Gates
If you did objective 5 (sniping all guards on the ground) you definitely killed the 2 guards whoever they are. Head back to the top of objective 5 building and just wait for Priboi to come out.