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