Probably the best boss battle in the game, the clash against Major Problem takes place in four different stages. The battle consists in shooting the lit lamps around de boss' head, killing flying bots, jumping on rock plataforms and walking around a small circle area to dogde cheese lava, driller and fire. Therefore, the best character to use is Night Cap, because of its double jump, fast and long range shot and its shadow ability. There are five checkpoints during the fight, that makes everything easier.
Now let's get to business:
1st stage: as soon as you arive to the boss area, shoot the flying bots to bring out the boss. At the beginning he has only one attack (cheddar missils). Use your shadow ability to escape. Keep on shooting the lit lamps around the boss' head and dodging cheese. The is a rock in the center of the area you are standing. Use it as your shield. After you hit him enough [checkpoint], an alarm will trigger and you will have to go up the cave. Just follow the path and shoot the TV Zombies that will appear. At the top, the flying bots will show up and and after you finish them, three small platforms will appear, leading to a new fighting arena. Remember to double jump. These three last platforms take a while to show up, but don't get desperate. There is plenty of time to jump across [checkpoint].
2nd stage: just as the previous one, the boss will repeat the same pattern but one new attack is added: a flame thrower. There is nothing to worry about, since the is a rock in the middle of the arena, to help you out. After you hit him enough, again [checkpoint], an alarm will trigger and you will have to go up the cave. Just follow the path and shoot the enemies. At the top, three small platforms will appear, leading to a new fighting arena. Remember to double jump [checkpoint].
3rd stage: now things get really CHEESY. There is no rock in the center of the arena to protect you against the flame thrower and the boss has a driller that comes from the ground to hit you, and we still face flying bots and cheese missils. Don't panic! Use your shadow ability and double jump to survive. There are some small plataforms around, that can help you against the flame thrower. If the boss spams its ground drills against you, use your shadow ability and run around the arena. Keep shooting the lit lamps [checkpoint].
4th stage: LAST STAGE. Hope you are still breathing. The main island is now divided in four smaller parts, connected by jumping platforms. There is no more driller but only cheese missils, flame thrower and flying bots. Give them all you have. Hit the lit lamps and kill the bots. Jump around the platforms to dogde the boss' attacks.
Damn, the fight is over, achievement unlocked.