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