Here is the full list of all 33 N++ (NPLUSPLUS) achievements.
Beat 10 Hardcore Stories
Beat an entire Hardcore Story
Get all of the All-Gold badges in every page of Solo
Explore the options menu.
Beat an entire column of Solo Legacy episodes.
Beat the entire expert row of Solo Episodes
Beat the entire bottom row of Solo Episodes
Die 5000 times.
Beat the entire middle row of Solo Episodes
Beat the entire top row of Solo Episodes
Kill another player using a rocket 5 times in a single MP Race episode.
Die in every possible way.
Die 1000 times.
Beat an episode from the bottom row without dying.
Beat an episode from the middle row without dying.
Earn an all-gold badge in an episode from the bottom row
Earn an all-gold badge in an episode from the middle row
Beat an episode from the top row without dying.
Earn an all-gold badge in an episode from the top row
Get all the gold in the Solo Introduction
Die by hitting the ceiling too hard.
Beat an entire column of Co-op Legacy episodes.
Beat an entire column of Co-op episodes.
Die 100 times.
Triumph over adversity.
Beat an entire column of Race episodes.
Die during the solo introduction
Beat an entire column of Race Legacy episodes.
Watch a highscore replay.
Complete All Hardcore Stories
Get all of the All-gold badges in every page of secret levels
Get everything in Solo mode
Get everything in the Ultimate Edition of the game