Different enemies show up in different levels, so you will have to play many different levels to level them all up; there is no one single level you should play.
My best success is playing on levels that have an easy to access invincibility star and using that to take out as many things as possible. You can also level up enemies in Toad Rally. The same tactic, playing the levels that have easily accessible stars combined with the long looping levels, is a great way to quickly level things up.
Keep in mind that some enemy types have a a very low population and will take a while no matter what you do.