Here is the full list of all 20 Downwell achievements.
Beat the third area (hard mode)
Beat the second area (hard mode)
Have more than 5000 gems
Land a 100 combo
Beat the first area (hard mode)
Beat the boss
Beat the fourth area
Beat the third area
Complete a level without killing any enemy
Land a 30 combo
Complete a level without landing
Have more than 3000 gems
Beat the second area
Complete a level without shooting
Complete a level without visiting siderooms
Complete a level without taking damage
Beat the first area
Land a 10 combo
Beat the fourth area (hard mode)
Beat the boss (hard mode)