To get a high score, you need to clean out the level, meaning kill all the enemies, collect as many coins as you can, destroy all the boxes you come across, etc. Basically, destruction is the key.

On the screen where you select the level, in the top right corner, you can find a list of all available combos. These are great for boosting your score.

You have to go through levels a couple of times to unlock new ones, so get ready to grind.

Tap the jump button quickly to make small jumps that are a lot more precise and useful sometimes.

Use dash to move over gaps.

Heavy attacks are pretty much useless. They don't do a lot of damage and take way too long to recharge.