Here is the full list of all 29 Rhythm Overdrive achievements.
You managed to finish your first song!
You already completed 10 songs!
You finished all songs in easy mode.
You finished all songs in hard mode.
You managed to get at least the S Rank in all songs in easy mode.
You managed to get at least the S Rank in all songs in hard mode.
You managed to get at least the SS Rank in all songs in easy mode.
You're now one of the best player of this game, congratulations!
You managed to get at least the A Rank in all songs in easy mode.
You managed to get at least the A Rank in all songs in hard mode.
You killed 50 000 enemies !
Finish one song with the yellow weapon as main weapon.
Finish one song with the red weapon as main weapon.
Finish one song with the green weapon as main weapon.
Finish one song with the blue weapon as main weapon.
Finish one song with the orange weapon as main weapon.
Finish one song with the pink weapon as main weapon.
You killed 1 000 enemies !
You killed 10 000 enemies !
You completed 30 songs !
You made a combo of 500 !
You made a combo of 1 000 !
You made a score of 5 000 000.
You made a score of 10 000 000 !
You made a score of 15 000 000 !!
You made a score of 20 000 000 !!!
You finished an easy song without getting hit once !
You finished a hard song without getting hit once !
You got all the achievements ! Congratulations !