As requested by some of my students I am setting out a few thoughts about writing essays and more particularly writing the minor thesis that is required for the Galway LL.M. This is of course a really vast subject and I can only make a few brief comments here.
The really key requirements are (in order of importance)
As regards delivering the goods remember the military maxim that a good plan today is better than a perfect plan tomorrow. You will not graduate unless you produce a thesis whether it is good, bad or indifferent. You are better off by far to knock out some kind of draft that can be discussed and improved before the deadline than to tinker indefinitely in search of perfection.
Also it is essential in any exercise of this kind to familiarise yourself with the actual regulations regarding submission dates, format, etc. Look it up and ask if you are unsure.
Having a "thesis" is the next most important item. An LLM or indeed an essay is not a showcase for you to recount all you know about some subject. You must have a thesis, an argument, a proposition that is to be backed up or falsified. It does not have to be anything terribly exciting but the whole thing must hang together - the disparate parts must relate back to a central argument. That argument in turn must credibly relate to the course, in other words it must be a proposition of law or legal theory. Bringing in other disciplines is fine if the final result can be related back to a legal proposition.
Originality is not a requirement of an LLM thesis but it is always nice to see. Originality is a broad concept and includes bringing new information to bear on an old issue - see the list of types of originality in Phillips and Pugh, How to Get a PhD, 3rd ed., (Buckingham, 2000) pp. 63-64.
Your insights and comments are important because by virtue of having been accepted as a university student you are a member of the academic community and your audience in writing is other members of the academic community, represented by those who mark your work (and those who read it if you publish it later). In the case of the LLM in public law the academic community is represented by your supervisor and the external examiner, and the University decision-making structures.
Writing well is also always good. Your work will be read by humans not robots so spare a thought for the person who has to read your work and make their job easier. Write in understandable language and lay your work out clearly. For example I suggest that you might indent the first line of a paragraph, skip a line between paragraphs, indent lengthy quotations (personally I would indent anything equal to or greater than a full sentence), write clear grammatical prose, familiarise yourself with standard footnote and citation styles and ask if you are unsure. For example report citations should generally be footnoted not embedded in the text. A good guide to legal writing is Chapter 14 ("Legal Writing") of Tom O'Malley's Sources of Law (2nd ed.) (Dublin, 2001) although bear in mind that O'Malley's presecriptions - no more than my own comments - do not have the force of statute law and as with many aesthetic rules the precise application will be a mixture of taste and skill on your part. Indeed complete mastery of the rules of aesthetics may be said to have been achieved when you know when to break them.
Keep these 4 objectives to the forefront and you will not go too far wrong.