Quest 1 - The Golden Bird
Quest Giver: No one in particular.
Begin by: finding a Jade Figuring in the wilderness.
Quest Location: Anywhere in Act 3.
Quest Reward: +20 infusion to your hit points.
When you begin the Act, you will have no quests in your quest log, even after speaking with everyone in Kurast. The first quest begins by wandering outside of town and defeating one or two unique boss monsters. You're not limited to a specific area, so wander around until you find one or two, and when defeated, one will drop a Jade Figurine. Take this to Cain, then to Meshif, who will exchange it for a Golden Statue that you should take back to Cain. Now speak with Alkor, once for the quest dialogue, and then again for your reward.
Quest 2 - Blade of the Old Religion
Quest Giver: Hratli the Smith.
Begin by: completing Quest 1 or entering the Flayer Jungle.
Quest Location: Flayer Jungle.
Quest Reward: A rare ring from Ormus.
After completing Quest 1, or by entering the Flayer Jungle, Hratli the smithy appears in his spot on the east side of town. Speak to him about Gidbinn the dagger. He'll ask you to recover it for him. Head to the Flayer Jungle and look for a Pygmie encampment with a statue pedestal in an open circular area. Activate it and a Pygmie boss will enter the scene. Those little guys hit hard. Defeat it for the dagger, which you'll then take to Ormus for your reward. While you're in the Flayer Jungle, keep an eye out for the Flayer Dungeon, where you'll need to go in Quest 3.
Quest 3 - Khalim's Will
Quest Giver: Cain the Elder.
Begin by: speaking with Cain after completing Quest 1 or entering the Great Marsh.
Quest Location: Spider Cavern, Spider Forest: Flayer Dungeon, Flayer Jungle: Sewers, Lower Kurast or Kurast Bazaar.
Quest Reward: A step towards entering the Durance of Hate.
This quest is similar to the one in Act 2 where you assembled the Horadric Staff. Begin by speaking with Cain after completing Quest 1 or by entering the Great Marsh. For this you'll need three pieces, plus the Khalim's Flail from Quest 5 and the Cube from Act 2. Khalim's Eye is in a golden chest in the Spider Cavern, within the Spider Forest, usually toward the end before entering the Flayer Jungle, but not the dungeon by the waypoint. Khalim's Heart is in the Flayer Dungeon, usually near the beginning of the Flayer Jungle area. Go down to level 3, which is set up like a long maze, and in the last room there will be some unique bosses and a golden chest. It's in the chest.
For Khalim's Brain, go to Lower Kurast or the Kurast Bazaar and find an entrance to the Sewers. It's a large dungeon but look around for a single switch to activate the stairs nearby down to level 2, which is just a large single room. The Brain is in a golden chest. When you get all three, go and visit Cain, and continue up the path in Act three toward Travincal, then see Ormus.
Quest 4 - Lam Esen's Tome
Quest Giver: Alkor.
Begin by: speaking with Alkor after completing Quest 2.
Quest Location: The Ruined Temple, Kurast Bazaar.
Quest Reward: +5 stat points.
Alkor, after completing Quest 2, will give you another quest if you speak to him again. To help fight the evil, he suggests finding a book called Lam Esen's Tome, which resides in one of the temples in the three Kurast areas. It's not necessary to look through all the temples in Lower Kurast, Kurast Bazaar, or Upper Kurast. It's always in the same one, called the Ruined Temple, in the Kurast Bazaar.
Before you go down, be prepared to be swarmed by enemies and a unique extremely quick boss. It's a small dungeon, and soon after you enter the enemies should come running at you. Find the Tome in the back room and bring it to Alkor for your very decent reward.
Quest 5 - The Blackened Temple
Quest Giver: Ormus.
Begin by: speaking with Ormus after entering the Kurast Causeway or completing Quest 4.
Quest Location: High Council area, Travincal.
Quest Reward: Stairs down to the Durance of Hate open.
After speaking with Ormus, you'll need to acquire Khalim's Flail, combine all four pieces, and smash the compelling orb. Enter Travincal, the most deadly area of Act 3, and the last that's above ground. You'll face a lot of powerful range attacks before you reach the High Council area in back. Try and systematically clear this area out, by not venturing too far, and then healing. Finally, when you get to the back, you'll face quite a few Unique High Council members, who fortunately will not all come running at you at once. If you have a range attack, stay off to the left and they'll be trapped behind the pillars, yet can still fire range attacks at you. Once they're dead, one of them will drop Khalim's Flail. Use the waypoint back to Kurast.
Put all four pieces in your Horadric Cube and transmute them into Khalim's Will. Equip Khalim's Will, and attack the compelling orb near the back wall of the High Council area. The entrance has been granted. Have a chat with Ormus for the final quest.
Quest 6 - The Guardian
Quest Giver: Ormus.
Begin by: smashing the compelling orb from Quest 5, then talking with Ormus.
Quest Location: Mephisto's Lair, Durance of Hate.
Quest Reward: Whatever Mephisto drops, as well as transport to Act 4.
When you smash the compelling orb, and speak with Ormus, you'll receive orders to kill Mephisto. You'll find him on the third level of the Durance of Hate. Once you take the stairs down, you'll receive an updated quest log to kill Mephisto. Before you reach him, however, you'll need to take care of a few High Council Unique monsters in the way. You can take the left or right paths around the blood lake to get to him. Once you're in combat with Mephisto, be aware of a ranged cold attack that's pretty powerful, but other than that, he's not the toughest boss. You can range him to death if you lure him to an edge of the blood lake and then run around to the other side. When he's dead, you can reach the portal in the middle of the lake by going over to the back end of the room, where a bridge of bones will appear, and walk across that to activate the portal to Act 4.