I know the title of this sounds weird, but this is an explaination.
While being in a group, and you are going for the achievement containing Group, then you may think "How to get the others to...", well - that's no more!
This allows you to solely get achievements that require a "basic" thing for groups.
Let's start with Intense Cold for an example - (This is 1man achievement, but this will explain like if it were)
"Defeat Keristrasza in The Nexus on Heroic Difficulty without allowing Intense Cold to reach more than two stacks."
WHOA, all the members need to do that? It's quite hard without a dispeller.
Look no further, heres the thing : If you do not get above two stacks, you will get the achievement if there is no one else "tagged" with you.
What is "tagged" with you? Players who were in a group with you first before going to the random heroic. If you went in random heroic with only you from the same realm, you are a lone player towards the achievement!
Short version :
Using Random Heroic, achievements that require the whole group to cooperative for a certain counter, will only affect you and not the other players. If the other fail, they fail. If you manage it, ONLY YOU will get the achievement.
This can only be worked if you don't invite players to come with you (as in the same realm).
I like to confirm more achievements working this way. I will update the list here as more get's found. I think the [Color] Void works this way too, if anyone want's to try that for a first.
-- I've Had Worse
-- Ruby Void (Halfly confirmed)