After the nerf for Act 2, 3 and 4, brought by the latest patch for Diablo 3, barbarians are viable after Act 1 for both soloing or in parties, melee classes are not getting one shotted after Act 1.
As attack speed was nerfed (IAS), clearing Act 2 with a 2 handed weapon is very hard now, if you can’t down a pack of champions during a Wrath of the berserker, 1 handed weapon and shield is the way to go.
First of, you should get a good shield, in Auction house, filter by +9% block rate, you will only see the shields that are blocking 3706-4706 damage. With around 500k gold, you can get a decent shield with at least 24-25% block.
With these stats, you can solo most of Act 2 but is far from being easy. 53k HP, 11k dps, 34% block chance, 8k armor, 500-600 all resistance (armor and resistance buffed). To finish Belial, you will need more DPS as now there is an enrage timer.
For skills, combining Earthquake with Wrath of the berserker is not a good idea until you can down one unit of a pack of champions within one use of these two skills. Earthquake can be replaced with Leap with the Iron impact rune for more survivability.
Barbarian Act 2 skills.
Revenge with Provocation rune.
Ignore pain with Iron hide rune.
Wrath of the berserker with Striding giant rune.
Leap with Iron impact rune.
Warcry with Impunity rune.
Frenzy with Sidearm rune.
For passive skills, Superstition, Tough as nails and Berserker rage.
Using the skills. Use Leap when is not on cooldown or you think you are about to take a lot of damage, Wrath of the berserker as soon as you engage in a fight with a pack of champions, in Act 2, they have a lot of CC, fire, you have to kite champions all the time.
If you reach the stats mentioned in this article, you can even pull all the map, or run to pull more mobs if you fight champions and you need a lot of light damage taken so Revenge will proc a lot.