Here is the full list of all 14 Spirits achievements.
Save the middle-left spirit in the "All for one" level
Collect 30 plants in any completed level
Complete "Cave Story" without using the 3 top-left spirits
Complete the "Three Paths" level by only using the blow action
Complete level 1 to 5 with perfect score
Complete the "Two sides" level without using the grow action
Collect a plant in any level
Collect 60 plants in any completed level
Collect 100 plants in any completed level
Complete "A Tree" level without any spirits dying against the spikes
Complete the "Downwards" level by only using the dig action
Complete level 6 to 20 with perfect score
Complete level 21 to 35 with perfect score
Complete level 36 to 43 with perfect score