Here is the full list of all 12 Storm achievements worth 400 gamerscore. It takes around 12-15 hours to unlock all of the achievements on Xbox 360.
Saved all Spirits
Finished the winter season
Break 5 seeds
Finished the autumn season
Saved two thirds of the Spirits
Saved a third of the Spirits
Created 30 tornadoes
Finished the summer season
Burned 20 grasses
Finished the spring season
Used bubbled 20 times
Do nothing for 30 seconds