Since this mission serves as a tutorial to introduce the player to Jak's arsenal of maneuvers and abilities, Daxter verbally guides you through the linear path of the fortress with the help of on-screen instructions. The guards blocking the path that are armed with tasers will not use their weapons in this mission.
Eventually you'll reach a room with a grating for a floor (right after the gap you had to cross with a long jump). You'll want to cross this as quickly as possible while sticking to the walls, as a large number of guards below will fire at you through the grating.
Moving on you'll only need to punch through two breakable metal gratings to reach an exit after a short slide into a waste-filled room. Climb to the stack of boxes to the right to exit the fortress and enter Haven City, immediately leading up to the next mission Protect Kor and Kid.