I am trying to express that X won a challenge. Which one(s) amongst the following are correct, which one sounds the best, and is there any better alternatives?
The two in the middle need to be adjusted slightly. The others are correct, but for the fourth one to be more exact and idiomatic, you should probably change it to "won first prize" instead of "place." First place is just a status that tells you where you are in the competition -- the prize is something that you win, because it is awarded to you upon coming in first place. "Coming in first place" means that you ended the competition in first place.
For the two in the middle, you need "in" between "came" and "first." "Came first place in a challenge" is grammatically incorrect. The third option, "came first in a challenge," is both a sexual innuendo and not expressive of what you want -- people will probably understand your meaning, but they'll giggle at the innuendo and know you're speaking broken English.
The first sentence is fine the way it is.
Alternatives
X won the challenge.
X came in first.
X placed first.
X is the winner [of the challenge].
