I think it's a fantastic slogan!

I slightly disagree with the other comments however.

Here the key factor is how it sounds, whereas all the other comments so far suggest the influence of the idea of correct English grammar.

Of course the other factor is if native speakers prefer it.

Here the answer is obvious.

One shot, one kill. No luck, just skill.

I added the full stop, since you want to help the reader to know that it's not any more a list.

The most effective speakers would also add a slight pause, to communicate the maning of the full stop.

And it definitely should be 'no', instead of 'not'.

Why?

It just sounds way better.

Say it yourself.

Your version with 'no' has better rythm.

(Yes I chose to write the last sentence in a more verbal and less correct way. Because it just sounds way better!)

Well, it would not be a sentence.  Assuming you are not wanting a sentence, just phrases that is more like a slogan, I think it should be: One shot, one kill.  Not luck, just skill.

If you want it as a sentence, you would need subjects and verbs.