Discuss how Elizabethan tragedy departs from Aristotelian formulations of tragedy.

I can give you a few details to help you on your way to an answer or "discussion," as you refer to it.  My answer will assume you know the basic characteristics of tragedy, such as tragic figure, tragic flaw, catharsis, etc.  All of these are contained in Elizabethan tragedy and were originated by and taken from the Greeks. 

Elizabethan tragedy did build on what it inherited, though.  I say "build on," but some might see this as a negative development, as a corruption, possibly, of Greek thought concerning tragedy.  In other words, if you view Greek tragedy as the highest level of tragedy, than variations from it might be seen as corruption.

Positively or negatively, though, Elizabethan tragedy does vary from Greek tragedy.

One place for you to start would be with a contrast between Shakespeare's Macbeth and his Hamlet. 

Macbeth is very much classical.  Fate plays a large part in the play, although it takes a slightly different form:  predestination/determinism and free will are the issues here.  And the form of the play is tight and streamlined.  The tragic flaw is evident and consistent, as is the need for cleansing.  From early in the play, Macbeth's treachery and tyranny is clearly evident, and the need for him to be destroyed is definite.  Ambiguities in motivation are not present.

In contrast, Hamlet, is "all over the place," one could say.  Fate does not play a role in the play, and Hamlet's tragic flaw is ambiguous (we know he delays in taking revenge, but numerous possibilities exist that might explain why).  For at least part of the play, the guilt of the antagonist, Claudius, is doubted.  And classical-like balance is not maintained.  The play, in a sense, rambles:  Hamlet has a chance to kill Claudius and doesn't, he is sent to England, he partly walks back to Elsinore and happens across a grave being dug, he seems to take forever to enact his revenge.  He also gets side-tracked and wastes much time worrying about his mother's role as wife to Claudius.    

Many consider Hamlet more romantic than classic. 

These two plays represent Elizabethan drama imitating classical drama, and varying from it.