When one writes a critical appreciation of a poem, one should identify the poem's central purpose (its "meaning") and the devices and elements it uses in order to convey this purpose. It can also help to identify the poem's historical context, as this can help us to determine why the poet would have made the choices he or she did. Finally, one must assess how effective the poem is in terms of achieving what seems to be its central purpose.
In writing a critical appreciation of this text, it seems important to note that it was published in 1919, just the year after the end of what was then called The Great War, because the world had never seen anything like it and no one could imagine that such a catastrophic conflict could ever take place again. The war resulted in what seemed like a loss of innocence in the West; people were disillusioned by the death and waste and mass destruction, far larger than anything anyone had ever known before. This helps to account for the references to "anarchy," as well as the chaos, the darkness, and the drowning of the "ceremony of innocence" in the poem.
It would also be important to address the allusions to Christ created by the poem's references to the "Second Coming." Understanding what is meant by this phrase helps the reader to understand why it would be shocking that a "rough beast" that "Slouches towards Bethlehem to be born" would be so dark and frightening, compared to what Christians typically expect. And this "rough beast," the product of our own evils rather than our grace, may help lead you to some opinion on how well the poem achieves its apparent intended purpose.