Habroxia 2

Can only be accessed after completing the game once:

After finishing all of the levels in the game, including the alternate routes, you'll unlock several boss fight stages.

Following those, you'll unlock the final boss:



After killing that, a red wormhole will appear on the map towards the right hand side. This takes you to New Game Plus! Go through it. (Don't worry - you can return whenever you like.

You'll be on a clear map, but this time the levels are slightly harder, with more enemies in them, and tougher variants.

Complete the very first level again, and this achievement will unlock on the results screen.