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