I'm a vet of AVM, so listen up-here is how you actually get to Kompressor's lair.
After you beat main, go back to the Afghanistan level and make sure you do it on tough or else it won't work. After the fifth wave of bots, go to the blue building and climb to the top floor-there should be a Helicopter waiting for you. Now, this only works in the fifth wave, so make sure after you've killed 25 soldiers to rush or you might be too late. Also, make sure you have some good weapons, like an AK or Akimbo- You'll need them later.
The Helicopter takes you back to the Daytime Kitchen from the previous level(Keep in mind Afghan is level 13, kitchen part two is 12, and the desert palace is 14), but now, you spawn in the shafts to get outside which were previously blocked. You'll have to fight some blockheads with hammers, but eventually you get outside, which triggers a cutscene in which Kompressor breaks through a rift in the sky.
Kompressor is very tough- he uses a variety of weapons and attacks, as well as making these huge falling brick pillars and such. If he gets you down, heal immediately, or he could kill you, and then you'll have to restart the entire thing from the Afghanistan level. You can dodge the pillars pretty easily, but his Bricktide attack is pretty tough, as well as the brick shield. so make sure you jump and dodge in time. If you keep on firing, he'll eventually roar and bricks will start falling from the sly- ignore them and keep on firing until he dies(He explodes). He'll drop a key and a clue, and the clue reads "In the dresser you'll find me, but not only after three."
Basically, you need to go back to the Bedroom(You can only save your inventory after beating it once, so make sure you have beaten the story once before you embark), where you fight Badspot. In stage three, when he unleashes OmegaSpot, instead of attacking him rush to the dresser's side entrance- there will be a staircase. Run in there, and you'll find a door- Use the key, and voila, you've unlocked Kompressor's lair, which has the coolest things ever:
1.Goodspot's Red Sword from the picture when you talked to the old man in the first level. It's crazy strong, and can be thrown when held which emits a Bricktide affect and basically kills stuff.
2.Kompressor's boots, which are pretty self explanatory- their his boots. It has great base speed and jump, but not the best defense.
3. And loads of other goodies like food, armor, and even a mini Kompressor to follow you around.
The lair is really cool looking, and you can go to it from the Extras screen now.
Enjoy!