Instructions
Use Illidan, Kael'thas and their forces to fight the Master of Pain. The Master of Pain can reincarnate after he dies, so be ready for a long fight. Once he is defeated, collect your loot and open the nearby cages to free the imprisoned troops. The extra units will help you to recover from any losses you have suffered during the fight.
Use Vashj and her naga to destroy the bases leading up to the Mistress of Torment. There's a Fountain of Health along the way, so take the opportunity to restore your troops to full health. Though the Mistress of Torment can be defeated only with Vashj, you may find it easier to send over Illidan or Kael'thas to help out. Leave one of them and some troops behind to defend your base. There are extra troops to be freed after this fight as well.
Combine your forces to bring down Magtheridon. Use all of your special abilities and items. This is the last fight in the campaign, so use everything you have been saving until this point. Magtheridon's stats are much higher than that of an ordinary Pit Lord, so it's going to take your entire army to defeat him. Once Magtheridon surrenders, Illidan will replace him as ruler of Outland and the campaign will end.