I've seen both "mission critical" and "mission-critical" used, and either is correct. It is in common usage in American English, so it is perfectly reasonable to use. Searching "non-mission-critical" on Google brings up results and definitions with both that usage and "non-mission critical", so I believe either can be used. "Not mission critical" would also be correct but sounds slightly more formal. As I said, "Non-mission critical" means the same thing but sounds more informal and soldier-like.
"No mission critical" would be grammatically incorrect, as "mission critical" is functioning as an adjective in the sentence, and "No" is used to negate nouns, not adjectives. For example: "There are no cats," vs "The cats are not present."