Here is the full list of all 16 INK achievements.
Are you OK? (Die 500 times)
Better show some respect (Defeat the Second Boss)
They just keep coming back! (Defeat 300 enemies)
What did it ever do to you? (Defeat the First Boss)
How can you be so bad? (Die 10 times in less than 30 seconds)
Welcome to INK. Good luck! (Die the First Time)
I've heard bad things about you... (Defeat the Third Boss)
Didn't see me coming now, did ya? (Defeat 6 enemies without touching the ground)
Nothing can stop you (Beat World 1 without dying)
How have you not had a heart attack yet? (Beat World 2 without dying)
You probably went through hell to get this. (Beat World 3 without dying)
I had a feeling something was here... (Find and collect 5 hidden coins)
Find 10 hidden messages (Find and collect 10 hidden coins)
Should hide things better next time (Find and collect 20 hidden coins)
You really are amazing! (100% the game)
Didn't know you could do that (Beat Level 66 without Double Jumping)