Here is the full list of all 48 Tobari and the Night of the Curious Moon achievements.
Clear World 2.
Beat the World 1 boss without taking damage.
Die 100 times.
Game over 5 times.
Find the secret goal in World 2.
Collect all of the moon shards in World 1.
Clear World 1.
Find the secret goal in World 1.
Clear the World 2 boss without taking damage.
Collect all of the moon shards in World 2.
Clear World 3.
Beat the World 3 boss without taking damage.
Collect all of the moon shards in World 3.
Find the secret goal in World 3.
Clear World 4.
Beat the World 4 boss without taking damage.
Collect all of the moon shards in World 4.
Find the secret goal in World 4.
Clear World 5.
Beat the World 5 boss without taking damage.
Collect all of the moon shards in World 5.
Find the secret goal in World 5.
Clear World 6.
Beat the World 6 boss without taking damage.
Collect all the moon shards in World 6.
Find the secret goal in World 6.
Have at least 100 lives.
Have at least 5000 coins.
Eat a lot of jellied yams.
Game over 20 times.
Die 1000 times.
Clear the game within 3 hours.
Clear the game without a game over.
Spend 10000 coins in shops.
Use every magic at least once.
Collect all of the moon shards in worlds 1 through 6!
Clear World EX.
Beat the World EX boss without taking damage.
Collect all of the moon shards in World EX.
Clear World EX within 7 hours.
Clear within 5 deaths or less.
Clear without buying from shops.
Clear World EX with under 100 deaths.
Found the two secret photographs.
Clear World 6 in under 65'00"!
Clear Vs Desunoya☆
Defeat the evil staff roll!
Clear all the other achievements!