In order to be the best fighter possible with Kiryu, there are a number of things you can do. Obviously, the best thing you can do is earn as much EXP as possible in order to boost Kiryu's Stats. The better his stats are, the more damage Kiryu will do to others in battle. On top of this, battling others is the best way for you, as a player, to learn all the controls and the best way to orchestrate combos. Fighting others, both to earn EXP and personal experience of the fighting controls, will pay off in dividends in the long run.
Oddly enough, drinking alcohol can also help Kiryu become a better fighter when in battle. It doesn't send the best message in the world, but drinking some liquid courage in moderation will help Kiryu do this very thing. You see, with just the right amount of intake of alcohol, Kiryu's heat orbs will actually fill up faster during a fight, allowing you to use activate his Extreme Heat Mode quicker in order to use his amazing take downs.
However, be warned, as too much alcohol will actually do more harm than good. For one, Kiryu won't be such a good asset to have in a fight if he can barely stand due to all the liquor in his blood. On top of this, mobs are also much more likely to start a fight with an inebriated Kiryu, which is never good when trying to work your way through the Main Story. If you accidentally drink to much alcohol, definitely try to sober Kiryu up with some water or a break from all the missions.