Before Dueling
When dueling with your barbarian you should have none or almost no wasted skills or stats. You should pick out your type of barbarian before you even start to put the points in. For example, a pole arm barbarian would have 20 points in whirlwind, 20 points in mastery of the pole arm, and 5-15 points in iron skin. This is basically the same with every kind of barbarian, every kind but the war cry barbarian. The war cry barbarian should have no points in whirlwind and should have a sword and shield, as this is the easiest and fastest weapon for the war cry barbarian. A war cry barbarian is good in duels because he can stun for a period of time and deal out a fair amount of damage with his war cry. Barbarians with spears have the longest range with their attacks, so never duel against one unless you are either another spear barbarian, or a war cry barbarian. The pole arm barbarians have the second most range, they should only duel against other pole arm barbarians or ones with less range, some other types with lower range are the mace barbarian and the sword barbarian.
Necromancer
When dueling a necromancer always try to avoid his bone spirit. The necromancer bone spirit can do around 400 damage at the maximum skill level if they have a few plus bone spirit or plus all skill level items. The bone spirits tend to go slow so if your barbarian has faster or fastest run/walk he should be able to avoid most or all of them when running. The necromancer can cast iron maiden if he is level 24 or higher, so if he does, RUN. There is almost no way you can defeat him if you have the iron maiden curse cast on you. The war cry barbarian can kill him if he stays a relatively far range when he uses the war cry though, but be careful. If you can, try and leap attack him while he's in the middle of casting something, if you hit him he is almost sure to die.
Amazon
The amazon is one of the best dueling classes in the game. Amazons usually use their guided arrows and guided arrows do a lot of damage. You should have about one thousand or more health if you are dueling an amazon level 25 or higher. If you have fastest run/walk boots and some points in the speed enhancing skill you might be able to run from the guided arrow, it will eventually disappear. If you can get the amazon in your sight jump attack on her. She might dodge the attack but it will stun her. Use that time to run right up to her and whirlwind through. If the amazon has a valkyrie there is almost no problem if you are a barbarian. The valkyrie has about 1500 life so you could kill it in one or two whirlwinds, or you could just ignore it and go straight for the amazon.
Paladin
Dueling the paladin is going to be tough but relatively simple. If he is a hammer paladin you should watch out for his blessed hammers spiraling out from him. When he has it a high level it will do a whole bunch of damage. He can also have plus skill level items and the concentration aura on. If he has these on he will do an amount of 400+ damage each hammer. That will be a death trap if you walk into the spiraling hammers. Another kind of paladin is the charge paladin. This kind of paladin also has concentration on most of the time but uses charge. He will come running towards you incredibly fast with images of himself behind him. When you see this happen, jump over him. If you stay there he will hit you and you WILL DIE. The charge paladin with a sword can do around 1500 damage, a charge paladin with a two hand weapon can do about 2500-3000 damage, so never get hit or you will surely die. Always jump over when he does it and whirlwind to kill him. Paladins also have thorns, so if he uses it don't attack, or run back to town, unless you are a war cry barbarian, as said before, you can kill him with a few yells.
Sorceress
A sorceress is nearly impossible to kill with a barbarian, but it can be done. If the sorceress uses frozen orb, just try and run away or jump over it. If you can, aim your jump attack to hit the sorceress for a certain kill. When and if the sorceress casts another attack, glacial spike for example, just jump to stun her and whirlwind into her. The sorceress has the ability to teleport also. If she teleports then try to catch up to her, and while she casts a spell, jump attack or whirlwind her in the small amount of time it takes her to cast a spell. These methods will be even harder if you have lots of lag or if the sorceress has fastest cast rate.
Other Barbarians
If you find yourself trying to fight another barbarian, make sure he has a lower or the same range as you, or he will hit you before you hit him. Also make sure you have lots of attack rating so you will be able to hit the opposing barbarian. If the barbarian whirlwinds from about 3 inches on your screen or farther away you will be able to dodge it by running to the sides and letting him go past you. When he goes past comes around and right when he stops whirlwinding whirlwind him before he has a chance to do it again.
Thank you for reading my barbarian dueling guide. I hope you benefit from what I have said because in Diablo2 you will most likely duel many times. Have fun with this game, I have had lots.