Inimical comes from roots meaning “not-friendly,” while inimitable means “not-imitate-able,” i.e. unique, or extraordinary, in reference to people.
Inimical can mean opposing, hostile, adversarial, or antagonistic:
Sunshine is inimical to depression.
Football fans are often inimical to fans of the opposing team.
Inimitable describes people with unique personalities and abilities—people who cannot be imitated (at least not well)—and it has positive connotations:
Please welcome to the stage, the inimitable Madonna!
Inimitable is used mainly in sentences like this one, introducing a famous personality.