I know this has been asked a thousand times, but I would like an opinion about my case.

I'm from Brazil and I'm about to graduate in Law.
My College is a very good one (perhaps top 10 in the country), but because of really terrible family and personal problems my grades aren't very good (I guess I could pull to 7,2 at most...that's something like a low 2:1 I guess).
Even though my grades are mediocre, I was granted a special permission to enroll at my college's Criminal Sciences postgraduation while I was still at the beginning of the (this) last year.
To summarize, my grades are around 7,0 (7,2 max), I will be graduating already with a specialization and I don't know if this has any relevance but I'm fluent in english and german (because I lived in germany for a year in an exchange program).

My next goal is to apply for a Master's (LLM or MA) in International Human RIghts or International Criminal Law.
I'm aiming (specially) at Lund's or Essex's International Human Rights course and Leiden's International Criminal Law.
Do I have any chance? If I'm going to try, should I explain the reasons for such bad marks?

Thanks in advance.

I would definitely try! Your level of English is a quite important parameters. Usually, universities know how dififcult it is to compare grades between countries, especially in places like Essex where about half the students are from different countries. And in the human rights field, good universities - which would certainly include Essex - will pay a lot of attention to your motivation, your experience; in a word, your capacity to make the most of your degree to make a difference int he world.

In a word: go for it!

I agree with Sylvain. Definitely go for it. Write a good motivating letter which explains the low grades and see what happens. Also, try to do well in this year's first term to show that you're dedicated. Do you have any other relevant experience, maybe working for an NGO? If not, and if you can with everything else going on, try to get an internship. Good luck!