Map of the area:
Map legend: 1 - starting area; 2 - decontamination zone; 3 - control panel; 4 - area where the first drone appears; 5 - room with a glass wall; 6 - ventilation shaft; 7 - elevator shaft; 8 - medical station; 9 - corridor (cut-scene)
Once you've regained control over Riddick make sure to have a hairpin chosen from your inventory. Start moving forward. Thankfully you won't encounter any enemy units along the way, because Riddick will only try in catching up to the rest. Proceed towards a small room [#409] and wait for a decontamination procedure to end.
Head on to a much bigger room and proceed to your right. There's a large control panel here [#410] and obviously you'll have to use it. Doing this won't unlock the next passageway, but instead it'll trigger a safety procedure. Go back to the crates quickly and take cover in the shadows. Wait for a drone to enter this area.
I guess I don't have to remind you that you should wait for the drone to turn its back on you. Leave your cover and kill your opponent. Now you must drag the drone to your right, so you'll be standing near a glass wall. Use drone's weapon to destroy the wall [#411]. Go to that area, ignoring smaller creatures in the area, Look around a little to find a bounty card (Jaybird Fries).
Don't leave this area just yet. Instead start climbing on some of the nearby crates. Once you're standing on the last crate look up to find a railing [#412]. Use the railing to get to the other side safely and enter a new ventilation shaft. Get to the corner to be rewarded with a cut-scene. Proceed to the end of the shaft and perform a well-know move by kicking out the grating.
Make sure not to fall down, because Riddick would die on the spot. Press the action key and the main character should automatically grab a pipe. Start moving to your right. Watch a new cut-scene when you get to the end. Climb up to get to a new platform and proceed to your right. You should be able to find a cartridge here, as well as a NanoMED health station [#413].
Use a nearby ladder to get down to a lower level (slide down). Make a few steps forward and make sure to hide in the shadows. Wait for one of the drones to show up and surprise it from behind [#414]. Take over drone's cannon and fire a few rounds to attract the attention of the second opponent. Wait for him to show up and kill him on sight.
Proceed to the corridor which has been patrolled by the second drone not long ago. Once again you must use a ladder to get down to a lower level. Press the action key and start moving forward while holding on to one of the pipes [#415]. Keep moving in that direction until you'll be given a chance to climb to a new hallway. Watch a new cut-scene.
As you've probably suspected, Riddick's top priority at the moment will be to gain possession of the blades. Turn around and return to the elevator shaft. This time you don't want to grab the ledge. Instead drop down [#416]. Open the ventilation shaft and you'll be rewarded with an interesting cut-scene. The blades are yours! :-)
Start moving forward and eventually you'll end up standing inside a small room. Notice a NanoMED health station on the wall [#417]. Get ready for a very challenging section of the mission. You can decide how you to want to play this all out...