The first thing to do is to find the door that will get you out of the vault. You can run a few circles around the baddies to get them to start fighting each other, then make your way to the western door, which is the only active one. Hit the switch , and get ready to take out two Hunters that guard the outside hallway. There are a few inactive transporters in this hallway - you should ignore them and then race towards the northern side, where you'll see another airlock. Use this to get out of the vault area, and slip through the rock to get to the surface, taking out the Enforcer that guards this area.
At this point, remember those Juggers you saw at the start of Mt. Vesuvius? Well, now they're training their sights on you, and are joined by some Hunters and Troopers. Do your best to ignore the enemy fire, and circumvent the volcano to make for the elevator on the southern side of the crater. You should be able to time your dodges as to jump on the elevator when it's in its lowest position, *and* in plenty of time to avoid the explosion and rising lava from the bomb.
Once safely at the top of the elevator, a short path will take you to the true exit transporter pad.
No secrets on this level.