Here is the full list of all 13 InkSplosion achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Kill your first enemy in hard mode
Kill 100 enemies in Arena Mode
Kill 75 enemies in Arena Mode
Kill 50 enemies in Arena Mode
Kill 25 enemies in Arena Mode
Reach 100,000 points in Classic Mode
Reach level 10 in Classic Mode
Reach 75,000 points in Classic Mode
Reach 50,000 points in Classic Mode
Reach 25,000 points in Classic Mode
Reach level 5 in Classic Mode
Kill your first enemy
Die for the first time