A cheap way to win big: Have more Samurai than Ashigaru ;)

If you're on the defensive and can find a nice hill, that's a guaranteed way to win big too, of course. I think the bonus you get from fighting downhill is pretty huge.

The key factor, imo, is to have the rock to his scissors, switching out units in the army to match the enemy army. This is hard to do of course, without serious scouting ahead, and not very feasible economically. If you're up against an all archer stack, you want to be heavy on the cavalry side. If you're facing only infantry, there's less need for cavalry and if you're facing a lot of cavalry, you want a lot of spears (duh).

I tend to win costly victories when my balanced stack comes up against a very biased stack and I for some reason fail to use my advantages and/or allow the AI to use the advantage of focusing on one kind of troop type. If you field balanced armies it's absolutely key to fight cavalry heavy armies in a forest, distract archer hordes with flanking cavalry while the infantry closes the distance without getting completely annihilated etc.

Other than that I don't know... Use the Inspire ability well? I like the Stand and Fight ability a lot, it's wonderful when you've parked your army on a hill. Your archers reload faster and your infantry gets a bonus to attack.

I've played a bit with splitting my force into two when the AI has allowed it. Basically, I was the attacker and the AI camped on a hill. He had fewer archers, but I didn't want to just engage him head on anyway, so I put all my archers out on a flank so they came at his hill on top of another forested hill. I put spears and two katanas behind them, and then a strong line of katanas and naginatas in front of the AI but some distance away. By moving my troops closer/further away from him on either side and hiding/revealing the archers in the forest I got the AI to constantly change his position at a run, tiring his troops out so the sandals by their banners were red or deep orange before the melee eventually began. By then I had managed to get some free volleys in from the archers on his flank. Major win. The tiring out part is a bit cheap though.