How to write an essay on critical analysis?
I believe what you need is not an essay ON critical analysis (in this case you have to write what critical analysis is, how to do it, why it is needed), but an essay, which IS a critical analysis.
If you critically analyze an issue or a phenomenon – just describe it in all details, consider it from different angles.
If this has to be a critical analysis of an article or a literature piece (this is the most common task in relation to “critical analyses”) – dig into
– the use of rhetorics (ethos/logos/pathos) – for an article;
– imagery and literary devices – for a poem,
– depiction of a particular character/topic – for a book.