If you collected the BFG on a previous map, rush the Spider demon with that weapon - it will fall in only two hits.
If you are starting with only a pistol and 50 bullets, you will need to use the available supplies. Run forward to collect the rocket launcher, and make a hard left turn. Keep running along the edge until you collect sufficient ammo, which should be when you reach the stairs. Then, run to the center, and open the center room to collect the blue armor and plasma gun. As with the cyberdemon, the spider mastermind is resistant to rockets, and takes more damage from plasma. Note that there is no room for error; you don't have that much ammo to eliminate all targets on the map, even if it is possible.
In addition, it is possible to defeat the spider mastermind by triggering monster infighting. You will need to have the mastermind hit both cacodemons and the baron of hell (which is not possible on Easy). If done correctly, the spider mastermind will either be weakened significantly or defeated by the three other monsters.
Secrets[edit]
There are no secrets on the map, beyond the helpful tip of opening the middle pillar for a plasma gun and blue armor.
Deathmatch[edit]
This map isn't designed for deathmatch. There are only the two weapons, and a single blue armor in the middle, and one of these weapons is hard to reach.