Trouble on status combination

Solution 1:

TL;DR: Invest in a good weapon, and dex/vitality for the rest of your gear; use the auction house to your advantage.

I found that high-ish vitality was the secret to success for nightmare (on my monk, so take my tips w/ a grain of salt). Also, farming the auction house for some choice items really helped.

Going into nightmare, I had a very damage-focused item set, and had maybe 2k health. I was dying left and right!

After investing pretty heavily in a great weapon and dex/vit gear, I had my health up to about 8k, and was able to breeze through the rest of the difficulty.

My tips are mostly focused around searching the auction house.

General AH searching tips:

Set a maximum buyout of 10,000 gold or so. There's always a ton of great deals; this also filters out everything that's bid only.
Always set filters when searching.

Invest in a good weapon:

Weapon power seems to stair-step every five levels, so find one that's got a minimum level requirement at the nearest multiple of 5. (e.g. if you're level 32, get a level 30+ weapon)
Focus on whatever stats you like on the weapons; As a demon hunter, I'm guessing that you want attack speed and dexterity.
You might want to spend a bit more (25,000 gold buyout or so); but check the cheap ones first, people often don't have a good understanding of the current market's prices.

Decking out your armor:

Filter to vitality, dexterity (and optionally something like gold find or magic find)
If you get 5+ pages of results, try raising the minimum amount of dexterity to reduce the # of results
Don't forget that each gem slot can effectively be a good 20-30 dexterity (mid-tier gems are cheap!)

Solution 2:

I would go with Vitality + Dexterity.

I had about 5k hp in Nightmare and was dying constantly. By the time I got to Diablo I had upped it to about 13k and my playing was considerably less, well, dead. Vitality is extremely important to any class, despite whatever the primary attribute(s) may be. Once you get to the harder difficulties having health is a definite necessity.

A combination I've recently discovered that goes well with Dex + Life on Hit (assuming you already have decent hp) is taking the Sharpshooter perk and some assorted +crit chance/damage, resulting in very frequent crits and essentially constant healing.

Despite attack speed not having a cap (as far as I know) and life on hit being very useful, you don't output nearly enough damage to sustain the damage Hell/Inferno enemies output. It's better to be able to take a few hits and escape than get (nearly or straight up) one-shotted by normal mobs later on and slowly regain health. However if you play a lot of co-op this may be more successful, although you would have to make avoiding damage a priority, which would detract from your damage output.