I found one of the best descriptions here, it's worth a read:
The serial bully displays behaviour congruent with many of the diagnostic criteria for Narcissistic Personality Disorder. Characterised by a pervasive pattern of grandiosity and self-importance, need for admiration, and lack of empathy, people with narcissistic personality disorder overestimate their abilities and inflate their accomplishments, often appearing boastful and pretentious, whilst correspondingly underestimating and devaluing the achievements and accomplishments of others.
Often the narcissist will fraudulently claim to have qualifications or experience or affiliations or associations which they don't have or aren't entitled to. Belief in superiority, inflating their self-esteem to match that of senior or important people with whom they associate or identify, insisting on having the "top" professionals or being affiliated with the "best" institutions, but criticising the same people who disappoint them are also common features of narcissistic personality disorder.
Narcissists react angrily to criticism and when rejected, the narcissist will often denounce the profession which has rejected them (usually for lack of competence or misdeed) but simultaneously and paradoxically represent themselves as belonging to the profession they are vilifying.
Fragile self-esteem, a need for constant attention and admiration, fishing for compliments (often with great charm), an expectation of superior entitlement, expecting others to defer to them, and a lack of sensitivity especially when others do not react in the expected manner, are also hallmarks of the disorder. Greed, expecting to receive before and above the needs of others, overworking those around them, and forming romantic (sic) or sexual relationships for the purpose of advancing their purpose or career, abusing special privileges and squandering extra resources also feature.
People with narcissistic personality disorder also have difficulty recognizing the needs and feelings of others, and are dismissive, contemptuous and impatient when others share or discuss their concerns or problems. They are also oblivious to the hurtfulness of their behaviour or remarks, show an emotional coldness and a lack of reciprocal interest, exhibit envy (especially when others are accorded recognition), have an arrogant, disdainful and patronizing attitude, and are quick to blame and criticise others when their needs and expectations are not met.
The DSM-IV Diagnostic Criteria for Narcissistic Personality Disorder are:
A. A pervasive pattern of grandiosity, need for admiration, lack of empathy, as indicated by at least five of:
1. a grandiose sense of self-importance
2. is preoccupied with fantasies of unlimited success, power, brilliance, beauty, or ideal love
3. believes that he or she is "special" and can only be understood by, or should associate with, other special or high-status people (or institutions)
4. requires excessive admiration
5. has a sense of entitlement, ie unreasonable expectations of especially favourable treatment or automatic compliance with his or her expectations
6. is interpersonally exploitative, ie takes advantage of others to achieve his or her own ends
7. lacks empathy and is unwilling to recognize or identify with the feelings and needs of others
8. is often envious of others or believes that others are envious of him or her
9. shows arrogant, haughty behaviours or attitudes