Here is the full list of all 16 Ink achievements worth 1,000 gamerscore.
Die the First Time
Die 10 times in less than 30 seconds
Defeat the First Boss
Defeat 300 enemies
Defeat the Second Boss
Die 500 times
Find and collect 5 hidden coins
Defeat the Third Boss
Defeat 6 enemies without touching the ground
Find and collect 10 hidden coins
Beat Level 66 without Double Jumping
Find and collect 20 hidden coins
100% the game
Beat World 1 without dying
Beat World 2 without dying
Beat World 3 without dying