To defeat the dragon is very simple. Hopefully by this time you have already gained enough levels to hold 1,000 health. If you have not yet gained enough levels, you may not be ready to defeat him.
First, gain at least 1,000 health – you may need it. Also, special items help kill him quicker and make it a less stressful experience. Especially helpful special items include: 3 way shot, super shot, invisibility, and invulnerability.
Defeating the dragon is very simple. Stand close to him, but far enough away so he cannot swipe you with his claws. Fire your quick attack continuously, and stop only to use special items. Be willing to sacrifice health.
The easiest way to kill the Dragon requires you to first go the store with plenty of gold. Purchase at least 2 3-Way Shots, 2 Lightning Amulets, and 2 Rapid-Fires. Be sure to enter the battle with the Ice Axe and be at level 30 or so. When the dragon is frozen, stand at a close distance and hit him with everything you got. At level 30 and with your upgrades, it's entirely possible to kill the Dragon before he unfreezes.