How Anonymous breaks Twitter security everyday to hack accounts?

The focus of this question is totally security so as my interest, so please do not report it.

How Anonymous hackers hacks into their desirable twitter accounts ?

I believe this is almost impossible to break into twitter database and pull out your desired account data, even if someone manage to do that, how would he be able to break the Hashing algorithm used to hash the password ?

So how does these Anonymous hackers hacks the Twitter account so frequently ?

The recent example of these hacks is,

http://ift.tt/14x8HbD

Are they really that good in breaking hashes or breaking the security of website like twitter ?