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