It's all Fun and Games until you hit Nightmare Level
It isn't easy being green. Or Arcane. Or Frost, for that matter. The first thing I found out that was once I hit the Nightmare level, Azumi folded like a cheap suit everytime ANYTHING came close to him. I got through the first few quests with only a death or two, but after I hit the Cathedral, things changed. I adjusted my build a bit more, and downed Magda. I was feeling really confident when, as level 38, I set out for Caldeum. I was confident with my play, confident in my gear, and ... just confident.
And once more, Azumi fell over dead within the first few mobs as soon as we hit Stinging Sands. After some tries (and a lot of repair bills), I came up with a reasonable strategy.
COMPANION: Enchantress. I actually hate this character (I wish she'd find a better fashion designer, for one thing (yes, this is the Girl Geek Gamer Snark) and I'm tired of her dialogue) -- BUT -- when it comes to noticing and controlling mobs, she's the best. I'd rather run with Lyndon the Scoundrel, but at Nightmare level he's not effective against the wasps. You remember the wasps. They're all over the desert and the oasis and they shoot baby wasps at you that explode on contact. The Scoundrel's slows really don't work on a large mass of mobs -- and believe me, at this level of Diablo, all the mobs seem to remember you from the first time around and show up with their buddies. Lots of buddies.
GEAR STATS: I had to start including Vitality gems. At this point, I'm wearing socketed gear (except for gloves, bracers, boots, belt which don't have sockets) -- including rings and amulets when I can get them. I look for anything that adds protection in addition to armor.
In general, these are good areas for leveling if you're careful and become pretty decent to farm for a bit once you hit level 44-45 (unless you're spending all your money at the Auction House. I'm writing for people who don't have a huge bankroll.) There's quite a few blue level mobs and gold level mobs and the area's big enough that you can run away from things if you get three blue levels and a gold level charging your poor little wizard all at once. The town teleport is your friend -- once you've taken down a big group and are not at full health, teleport back to town and have the priest bless you up to full health.
Sadly, all the things I really want are not available simultaneously. Hydra is incredibly useful if you can run mobs past it but, sadly, you have to give it up if you want to slow and damage mobs with Blizzard. I love having the Familiar -- but when you're in the caves, keeping Ice Armor up is a good safety measure because it freezes a lot of the mobs when they hit you. Archon is a necessary spell because it WILL level just about anything if you can get to it in time. The problem is, it only lasts for fifteen seconds. This is a problem when you have a pack of 40 demons plus a group of three scaly casters and a gold monster all chasing after you. Eventually the spell runs out, everything is half dead and thoroughly annoyed and they're coming after YOU.
Cave of the Betrayer/Vault of the Assassin (get Kulle's blood)
The quest isn't that hard at level 44 -- IF your armor's good and you're doing 1.5k damage or better. As for the rest of us, we usually have to make some awkward stats tradeoffs when gearing up. Expect to die several times, as multiple elite mobs usually lurk in the same area and they have lots of friends waiting with them. Take along plenty of health potions.
In using Ice Armor, you want to make sure that one of your passive skills is "galvanizing ward", which increases the duration of your armor and grants you life regeneration. Evocation, which reduces cooldowns, helps a bit with the Archon spell. I picked "cold blooded" since I'm using a lot of frost magic but you would pick conflagration or paralysis if you're doing damage with fire or electricity. Spells that had been reasonably effective (magic missle, for example) are pretty much useless -- you'll want to stick with the continuous cast beams.
When you see blue and gold level monsters, do NOT stop and ask, "Do you feel lucky, punk?" Switch to Archon and blast them to pieces (after putting up a slowing field.) Then hang around and admire the loot after they're dead until the cooldown on Archon is gone before you move ahead.