I few minutes ago on NHK news 「注目」 I've heard/saw the phrase 「やるっきゃない」. I have no idea what it means.. And what grammar rules are here?
っきゃ is an informal spoken contraction of しか, a particle. やるっきゃない means やるしかない.
The particle しか is always followed by a negative of some sort, either an explicit negative like ない or a predicate that is semantically negative such as だめだ or あるもんか.
Taken together, しか＋ない means something like "only; nothing but". It commonly follows nouns, but it can follow other sorts of constituents as well. When it follows a verb, it means that the verb must be done or will unavoidably happen (= "there is no alternative to 〜"). Your example やるっきゃない means something like "have to do [it]".