Can a player kill CONCORD?
Can a player kill CONCORD on his own?
Are their any Corporations/Fleets that have done an assault on CONCORD?
Solution 1:
In the past this was possible -- see here. A google search for "zombie siege of yulai" should turn up a lot of old discussions.
These days it is generally believed to be impossible to destroy even a single ship (the weak "concord" ships you destroy on pirate quests do not count), let alone the whole corporation!
Solution 2:
As a warning, even if you do (and you can't any more), it's considered an exploit and you will be banned for it.
Solution 3:
You will not get banned for attacking or even killing a concord ship. The concord ships are very strong and hard to kill, but if you do get one down they will send four more to replace it.