From the starting area, turn right (east) into a water pool. Kill the chaingunners and press the gargoyle-faced switch. Then return to the starting area, and go straight down into the lowered pathway. Take the first right to find a lowered platform (#1) holding a rocket launcher.
In the outdoor area in the west portion of the map, there is a ledge with the yellow key. Head southwest and step into the water pool. Turn around the corner on the right to find a soul sphere (#2). An arachnotron will then teleport in to attack you.