Combos only work in continuous lines, so don't try and curve them together.
If you wait for more than one object to spin up into the air will give you a whole line of objects to slice through and a much bigger points combo bonus in the process. It pays off to wait a bit.
The key to clearing out the screen sometimes is to use finger taps as well as swipes. If an object is about to disappear off the screen try using a quick tap to take out the problem.
Every time an enemy touches the bottom after launching into the sky, you'll lose a little bit of your health.
When you see the numbers 3, 2, 1 appear in succession you can expect a boss to descend on the action. The best way to take the bosses down is to simply swipe absolutely frantically back and forth over them.
If you want to unlock other stages in KingHunt, you'll need to beat some of the challenges of earlier stages.