How do you level up fast in Mario and luigi bowser's inside story?

Well, the long and short of it is, there is no quick and easy way to do it. The stronger you get, the fewer star points your enemies give you. Really, if you wanna level up, the best way to do it is to just fight enemies until they stop paying out. In other Words, I'd say:

Quick- Fight powerful enemies.

Easy- Fight a lot of weaker enemies.

There's not really a very reliable combination of the two.