Here is the full list of all 21 Retro/Grade achievements.
Beat the game on the X-TREME difficulty
Beat the game on the Tough difficulty or harder
Beat the game on the Beginner difficulty or harder
Beat the game on the Casual difficulty or harder
Beat the game on the Mediumcore difficulty or harder
Beat the game on the Pro difficulty or harder
Get a Continuum Captain rank or higher on all the levels in the Beginner difficulty
Get a Continuum Captain rank or higher on all the levels in the Casual difficulty
Get a Continuum Captain rank or higher on all the levels in the Mediumcore difficulty
Get a Continuum Captain rank or higher on all the levels in the Pro difficulty
Get a Continuum Captain rank or higher on all the levels in the Tough difficulty
Get a Continuum Captain rank or higher on all the levels in the X-TREME difficulty
Get an Astro Admiral rank on all the levels in the Beginner difficulty
Get an Astro Admiral rank on all the levels in the Casual difficulty
Get an Astro Admiral rank on all the levels in the Mediumcore difficulty
Get an Astro Admiral rank on all the levels in the Pro difficulty
Get an Astro Admiral rank on all the levels in the Tough difficulty
Get an Astro Admiral rank on all the levels in the X-TREME difficulty
Get to the end of the challenge mode map
Complete 50 challenges in challenge mode
Complete all the challenges in challenge mode