Here is the full list of all 20 Lantern achievements.
Completed the Summer Level.
Deciphered the temple in the summer land.
Found the first Sign Stone
Color is returning to the summer land.
Completed the Atumn Level.
Completed the Winter Level.
Completed the Spring Level.
Spread color and joy to the summer land.
Color is returning to the autumn land.
Spread color and joy to the autumn land.
Deciphered the temple in the autumn land.
Color is returning to the winter land.
Spread color and joy to the winter land.
Deciphered the temple in the winter land.
Color is returning to the spring land.
Spread color and joy to the spring land.
Deciphered the temple in the spring land.
Deciphered the temples across the entire world.
Used the Explosion Ability a total of 20 times.
Used the Speed Boost Ability a total of 20 times.