Alexander the Great does deserve his reputation. He accomplished a great deal at a young age. In addition, he was not simply a conqueror. He was also very smart (as befits someone who had Aristotle for a tutor) about how he dealt with people.
Alexander deserves his reputation because of his ability to build a huge empire. This was done partly through his military abilities. However, it was also accomplished by his ability to gain the loyalty of the people he conquered. He did this by doing things like allowing a large degree of self-rule to the conquered.
Alexander was not perfect by any means. He made mistakes that helped erode his support among his own people. However, his achievements certainly make him worthy of his reputation.