Based on the variety of Shakespeare’s works, how can one demonstrate that he is an outstanding writer?

The first piece of evidence that you should cite in favor of the claim that Shakespeare was an outstanding writer is his critical reception. He has become one of the standard authors read by all people studying English literature and his plays are widely performed. He has been translated into most of the world's languages and his complete works are available in numerous print and web editions.
Shakespeare wrote plays and poems, but not prose fiction. His poetry includes both long narrative poems and numerous sonnets. He contributed significantly to the development of the English sonnet, so that now the standard English sonnet consisting of three quatrains and a couplet is known as the Shakespearean sonnet. 
Shakespeare's plays include comedies, tragedies, and histories. He is one of the pioneers of "mixed" genre plays in which tragedy or even romantic comedy includes interludes of broader comedy involving "rustics" or other lower class characters. He was a very prolific dramatist and has a greater variety of characters and plots than most other dramatic writers.