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