Should I mention an academic achievement on my personal statement, even though it was in an area that is not directly relevant to the subject I am applying for (law)?

Yes, this provides a really good opportunity to demonstrate to the College not only your academic proficiency (in the fact you gained the award in the first place), but also that you are able to apply the sort of reasoning they are looking for.  In explaining why the achievement shows that you are a good candidate even though it is not directly related to law, you will be practicing the sort of reasoning by analogy and evaluative thinking that is demanded in the study of law.  Therefore while it will be a great thing to mention, it is equally important to think about and then clearly explain exactly in what way it is relevant and how it shows that you are a stronger candidate.