This is a small map, and the objective is simple - defeat the Mancubuses, then the Arachnotrons.
On the easier difficulties, there are two Mancubus and four arachnotrons. On moderate, there are four mancubus and eight arachnotrons. On the hardest ones, there are seven mancubus and twelve arachnotrons.
Up to four mancubus will appear on the raised platforms, with any extras on the main ground. If you need to lower a platform to get access to the item, flip one of the switches in the arena; each switch will lower a platform on the opposite corner.
When all mancubus are killed, the outer arena walls will open. The Arachnotrons will move in from all four directions and attack. The outer arena will also contain some items that can be used as well. When the arachnotrons are killed, the center platform becomes accessible.
When you start the map, quickly move to the left to pickup the backpacks, and to the right to collect the super shotgun. Try to obtain the plasma gun, as it inflicts significant damage per second, and has a lot more available ammunition. You may still want to collect other items to help recover health.
If you have trouble with the Mancubi, you can hide behind the solid walls to block their flamethrower shots; there is no worry about splash damage, as only a direct hit will injure you. Before you get the plasma cannon, you will have to hide behind the wall frequently and retaliating shots with the double-barrel shotgun.
When the Arachnotrons arrive, you can head into the outer area, and fight them off only three at a time.