Context: a boy is always been a head shorter than a friend of his, and he always said:
いつか、必ず抜いたるけんな
which I think I can quite understand ("Someday, I'm sure I'll surpass him"), but not really, since the whole 抜いたるけんな baffles me.
I did some research, and I found that けん can stand for から, but I'm not sure this is the case (see later).
About たる I found a couple of questions (this and this) which don't quite seem to apply, since in the first the structure is different (stem-たる, while above is short past-る), and in both is attributive, while above it doesn't seem so (unless it's attributive to けん, in which case it doesn't mean から and I don't understand it's meaning).
About な I think it's just and ending particle, maybe for emphasis.
抜いてやるimply in this case? It doesn't seem to fall in any of the meaning you gave in the other question; it's just likeThe sentence probably just means "I'll do that" (without "for someone"), so it just means he will grow taller, without "for someone"?