skipping the hazard shield: phazon harvesting
Walk forward as you enter, until the wall on your left is no longer visible. Turn left and do a quick screw attack to the ledge (you'll end up there after falling even if you don't make it). From here, you can see that the bridge ahead looks like it has several segments; get a running start and try to space jump straight to the second part. The rain damage will start as soon as you jump out, so when you land, screw attack to the corner past the bridge when you can get the height to make it. If you don't get off the bridge fast enough, expect the rain damage to rapidly increase after the first two seconds.
Once past the bridge, you should be in a safe spot. Turn around and space jump to the next two ledges, keeping to the right. When you land at the second ledge, go in the corner to cut off the rain damage. Turn left and screw attack just to the right of the bridge, and you should be placed at the door after falling.