"Look, Your Worshipfulness, let's get one thing straight. I take orders from just one person: me."

For the most part, Han was interested in two things. One was the girl. The other was the reward he got for saving the girl.

So when he blew away a nasty piece of work in the cantina, or attacked legions of stormtroopers in their own Death Star, it was in an effort to achieve the above and not because of a desire to do good.

Thus, it wasn't until the big finish that Han made the leap from reluctant hero to fully fledged legend.