Barbarian
Run when Diablo is about to launch the Lightning Inferno, then go back and fight. Use your leap attack because you cant be hit when you are actively Leaping. Stock yourself with Rejuvenation potions.
Necromancer
Use a golem to distarct, then curse Diablo with Amplify Damage. The lesser Necromancer minions are largely wasted on Diablo, so use a golem to distract and attack with anything you got. Bring along rejuvenation and mana potions if you plan on using Poison or Bone Spells.
Sorceress
Use meteor skill plus Static Field to knock down his hit points quickly. Static Field takes your enemy's hit points down by 1/3 every time you use it. That is a lot of hit points in Diablos case. Bring a lot of mana and rejuvenation potions.
Paladin
Use Thorns for the same reason the Sorceress uses Static Field. Every time Diablo hits, the damage will be returned. Bring health and mana potions also.
Amazon
Put some points into Decoy skill to keep Diablo distracted. If you have a bow then fire Immolation Arrow with a Long War Bow or Heavy Crossbow. Her battle strategy can be summed up quite simply, hit and run. Points into passive skills such as Dodge, Evade, and Critical Strike are also crucial to secure victory. Bring potions with you.
*from the Diablo 2 Ultimate Strategy Guide