What is a Double Perfect?

I recently noticed an achievement in Runner2 called "Double Perfectionist". The text says I need to:

Get two Double Perfects in Each World

Problem is, I have no idea what a Double Perfect is, let alone how to get one.

What is a Double Perfect, and how do I get one?

A double perfect is getting a perfect twice in the other game dificulties. That is, Rather Easy, Just Right, and Rather Hard.

To start off, getting a perfect means getting all the gold bars within a level AS well as getting all the score multipliers (mode UPs).

Getting a perfect on "Just Right and Rather Hard" or "Just Right and Rather Easy", or "Rather Easy and Rather Hard" in 2 levels of each world will get you your achievement.

As you may or may not already be aware, Runner 2 has three separate difficulties: Rather Easy, Just Right, and Quite Hard. Unlike in Bit.Trip Runner, where the difficulties merely altered the speed / collection requirements, the various difficulty levels in Runner 2 adjust the level itself, by adding enemies.

The other half of explaining this involves a brief explanation of the Perfect System itself - Collect all the gold and mode+ on the level (regardless of checkpoints, loops, or alternate paths), and you will score a perfect! If you reach the bonus cannon after crossing the finish line, you have gotten a perfect on the level. (Going on to then score a bullseye earns you a Perfect+, which is also tracked, but irrelevant to this question).

So a Double Perfect is earned when you have earned a Perfect on two of a level's difficulties, and a Triple Perfect when you have perfect!'d all three. Perfect!s are marked on the world map's levels as you achieve them, appearing as a colored exclamation point - Yellow ! for Quite Easy, Blue! for Just Right, and a Purple! for Rather Hard.

This means, to get the achievement you quote, you would have to beat 10 levels (2 in each world) a minimum of 3 times each (one for each difficulty)