What should I include in a critical study when aiming for an A or A* grade?

Critical studies are your opportunity to show the examiner that you can engage intelligently and critically with the work of other artists. Rather than giving an artist biography, it is important that the study focusses on the techniques used, and how these techniques function to get across a particular point or essence in the work. Also, you should try to demonstrate how this artist is relevant to your process and what you aim to take away from the study. A great place to start is by having a go at using the artist’s style and techniques to create a piece from your own source material; this could then be used as an interesting background for the critical study, and instantly connects the artist’s work to your own.  Writing a critical study can be daunting. However, it really doesn’t have to be very long- 100 well written words giving a concise and insightful analysis is far more valuable than two pages of waffle. Try to keep sentences short. Think about the processes used, textures, colours and surfaces. If the artwork you are looking at is conceptual rather than aesthetic, try to find some reliable information about the content; what was the artist trying to say, and how successful are they in conveying this message? 
Lastly, it's really good if you can briefly mention how this work is relevant to your own project. It could be as obvious as the study material, or as niche as a particular colour that sparked your interest. 
Another top tip is to not be afraid of dropping in a tiny critical study every so often, for instance an image of a painting and one sentence to explain its relevance. Doing this can show your examiner that you are constantly thinking and engaging with art and recognising links between your own style and that of others.