If I dodge, absorb, or block an attack, did I get hit?

For some of the "Challenge" achievements, the specific challenge revolves around killing a boss without getting hit, or hit by specific attacks:

It occurs to me that loading up on dodge and/or block might save a boss run for this achievement if I get particularly lucky. I'm not sure if this counts, though. If the attack intersects my location, but I took no damage (ie, I dodged or blocked), does this count as getting hit?

How do abilities that absorb damage change things? Can I keep something like Diamond Skin on and "cheat" that way?

In terms of the achievements, not getting hit means not taking damage. Using abilities like Smokescreen (pure immunity) counts, Diamond skin (absorption) also counts, dodging counts. Block does not count. In the case of block you're only reducing the damage taken rather than avoiding it.

For example, on the Belial encounter I have got the 'bad breath' (avoid being hit by his flame breath) achievement on both a Wizard and a Demon Hunter through the use of their immunities - no moving, just saw the attack coming and popped a cooldown.

So yes - you can use immunity abilities to get these achievements, and a fluke dodge will count towards the achievement as well.

Dodging definitely does not count as getting hit, as I just got that achievement as a monk (with ~40% dodge chance) and saw 'Dodged' for many fist attacks.

EDIT: Ignore this, I missed the Inferno difficulty requirement in the achievement.

No, a hit is when the monters hits and hurts you, if you move, block, dodge or something like that it doesn't counts.

I will have to do some tests, but I'm fairly sure that a "hit" counts when a monster hits you, regardless of the end result to your hp

So dodging will not count as a "hit", however blocking or absorbing the damage will