Here is the full list of all 41 DYE achievements.
Defeat the Ice Golem
Die 1,000 times
Collect 100 Pigments
Die 500 times
Float for 10 minutes
Defeat the Vultures
Get all 5 pigments in under 40 seconds on any HARD level
Die 100 times
Gather all pigments on HARD mode for a single level
Float for 1 minute
Drown in the first level
Die.
Get all 5 pigments in under 30 seconds on any NORMAL level
Complete each Purple level on HARD mode with ALL Pigments
Complete each Blue level on HARD mode with ALL Pigments
Complete each Green level on HARD mode with ALL Pigments
Complete each Red level on HARD mode with ALL Pigments
Gather all Pigments on HARD mode on ALL levels
Finish all Purple challenge levels
Finish all Blue challenge levels
Finish all Green challenge levels
Finish all Red challenge levels
Finish ALL challenge levels
Collect all Purple world Pigments
Collect all Blue world Pigments
Collect all Green world Pigments
Collect all Red world Pigments
Collect ALL Pigments
Defeat Inferno
Defeat the Slime King
Defeat ALL bosses
Collect 200 Pigments
Kill 2 vultures before the 3rd awakens, finish the fight
Defeat the Ice Golem in 100 seconds or less
Defeat Inferno after having 2 skulls active at once
Defeat King Slime without taking shrooms
Finish all Purple challenge levels on HARD mode
Finish all Blue challenge levels on HARD mode
Finish all Green challenge levels on HARD mode
Finish all Red challenge levels on HARD mode
Finish ALL challenge levels on HARD mode