Arcade Mode is open from the start, but you need to play through Adventure Mode in order to unlock the stages within.
These are the same stages as Adventure, though you can play for leisure or high scores.
When you have the choice to pick one of multiple stages, picking that stage will unlock the respective level for Arcade.
|Nanobreak||Complete Challenge Set A|
|Nanogrid||Complete Challenge Set D|
|Nanorush||Complete Challenge Set B|
|Nanotorque||Complete Challenge Set C|