How can I write a sufficiently detailed essay in the short time space given?

The key to nailing timing largely comes in making sure you are answering the specific question asked as precisely as possible. Often the time given seems so short because lots of writing time is spent addressing things which aren't directly pertinent to what you need to be answering. Therefore, strange as it may seem, taking a few minutes at the start of each essay to consider what sort of an answer needs to be given can save a lot of time! Further, taking five minutes to plan is highly recommended. Knowing the points you want to make before it comes to making them tends to mean you can expend more mental energy on expressing those points clearly, not on hurriedly trying to find something vaguely relevant to say. Also, don't feel the need to make your essays longer than they need to be. Short, direct essays are always preferable to those which are flabby and packed full of extraneous detail.