Here is the full list of all 47 Balan Wonderworld trophies - there are 31 bronze, 13 silver, 2 gold and 1 platinum.
Collect all trophies
Defeat a Lanced Plenti
Defeat a Lanced Nessi
Defeat a Lanced Multipli
Defeat a Lanced Endlessli
Defeat a Ghostli
Complete every round of Balan's Bout ranked "Excellent"
Collect every gold Balan statue
Defeat one thousand Negati
Collect every multicoloured Balan statue
Play every mini game in every chapter
Collect every costume
Complete every Act Three
Populate the Isle of Tims with one hundred Tims
Perform on every stage
Bring the Ultima Tim into the world
Complete the Tower o' Tims
Defeat Lance
Complete Chapter Twelve
Complete Chapter Eleven
Catch a fleeing cast member
Collect fifty costumes
Complete Chapter Ten
Complete Chapter Nine
Complete Chapter Eight
Complete Chapter Seven
Collect over one thousand drops in a single act
Complete Chapter Three
Discover the Father Tim statue
Perform on a stage for the first time
Complete Chapter Six
Find your way backstage for the first time
Complete Chapter Five
Collect twenty costumes
Defeat five Negati in a row
Complete Chapter Four
Populate the Isle of Tims with thirty Tims
Collect your first raindrop
Complete Chapter Two
Complete Chapter One
Defeat a Negate-guarding Negati for the first time
Unlock the Tower o' Tims
Feed a drop to a Tim for the first time
Play a round of Balan's Bout for the first time
Defeat a Negati for the first time
Collect your first Balan statue
Don a costume for the first time