Enter the school from the backyard. The goth kids cleared the path for you so loot the bodies there and order Jimmy to open the alternate path for handicaps. As soon as you enter the kitchen, turn the stove on, go to a short distance and use Cup-a-Spell to blast the oven, freeing the chinpokomon inside. Collect the items then leave the place.
Once you're in the dining hall, go behind the food counter and collect the items, including the key to the Chef's Old PO Box. You can loot that box later in the Post Office.
Exit to the south to reach the battle area. You can buy recovery items from the vending machine. Go to the right and enter the door that says “In” to access the Terrance and Philip bag in the previous room. You won't be able to past the barricade to the left easily because the enemies are using a water cannon.
First, knock out the guard near the hydrant by shooting the dangling flourescent lamp overhead. After doing that, shoot the leaky pipe to electrocute the other kid holding the water cannon. You can also flank them by using the vent nearby.
There's another blockade you need to get past. Enter the vent and use the alien probe to reach the upper vent past the barricade. Hit the vent cover to knock down one kid below. Use Cup-a-Spell on the torches to blast the path open. Don't forget to loot the Necromancer Gloves from the kid that got hit by a vent. Exit through the door.
There's another barricade waiting at the corridor and you can't use your Cup-a-Spell to blast it because of the electric fan installed there. You can shoot the water sprinkler to short-circuit the fan then use Cup-a-Spell.
For more loot, shoot the vent cover on the ceiling then use the alien probe to reach the vent. Once there, you can lure the rat to the mousetrap to avoid combat. Go to the south to find another chinpokomon and item bag.
Shoot the cable to make the fixture fall down on the unsuspecting kid below, then use the probe to teleport to the pipe and reach the small loot bag there. Rappel down to the floor using the cable. Head to the basement next.
Here, you'll encounter hallway monitors turned into nazi zombies. Defeat them in battle and loot the items. Exit the room and continue to the right. Smash the pipe then climb the ladder. Shoot the red valve to stop the water flow.
Enter the vent hit the vent cover to knock out the nazi monitor below. Now shoot the electrical panel to the lower right to make it combus, the use Cup-a-Spell to blast the walking nazi monitor when he's near.
Climb down the ladder then destroy the wood panel cover the ventilation maintenance access gate. Open the gate then turn off the generator. Go past the puddle quickly since the generator will kickstart automatically in a few seconds. Defeat the last remaining enemy then pull down the lever to shut down the generator.
The Boiler Room to the north has one of Jimbo's game targets. Head inside and place the rubbing alcohol on the green culture dish to trigger the battle. This should be an easy battle even if the enemy has enormous amount of HP. Use multiple status effects, preferably Froze, Burning and Bleeding damage.
Leave the room and continue to the right. Loot the items there and go upstairs. Exit through the door. Loot the bodies here then exit through the door as well.
In the next area, your enemies will be raining down fireballs at you. First, smash the blackboard to knock one enemy out. Head to the north and use the alien probe to reach the upper ledge to loot the item there. You can slide down and stand near the barricade to set it on fire. Blow it up with your Cup-a-Spell or Dragonshout but you need to be prepared of the incoming enemies.
After defeating them, use the catapult to set the fire on the barricades to the south. Now use Cup-a-Spell or Dragonshout to blow the obstacles and clear the way. Next, open the main door and continue north.
If you sided with the Elves, you'll be fighting Paladin Butters as soon as you open the door. (Siding with the human faction will pit you against Stan instead) Break his shield and block his powerful attacks. You can't do much damage on him so you'll have to rely on multiple status ailments to defeat him.
After the battle, loot the bodies and follow the enemies upstairs. Defeat all enemies ganging up on one of your allies. Next, head to the right and open the only unlocked locker to find a chinpokomon.
Head to the left and defeat more enemies. Once done, continue to the left. Enter the fifth grade room to find and befriend Lemmiwinks inside.
After that, leave the room and enter the fourth grade room. Here, you'll be given a choice either to attack Cartman or Kyle. Before doing anything, loot the room, including a chest to the left that contains a Laser Sword and a cool sticker. Hit the one you want to fight and defeat him in battle.
After the battle, watch the following scenes. The quest will be complete.