There are 50 Trophies that can be collected.

BRONZE

Escape King
Clearaed the escape tutorial

Poverty Elimination King
Saved 100,000 Bol and built your first workhouse

Half-baked King
Cleared Liam's tutorial

Graveyard Submonster
Obliterated Cow Bones

Upchuck Forest Submonster
Obliterated Yvonne

Wavy Rock Forest Submonster
Obliterated Clockwork Knight

Owl Forest Submonster
Obliterated Owl Yamanba

Tom Forest Submonster
Obliterated Ogre Ergo

Mushroom Forest Submonster
Obliterated Mush Bro

Red Turnip Forest Submonster
Obliterated Radeeze

Shadow Forest Submonster
Obliterated Mush Geezer

All-time Submonster Champion
Obliterated Blue Dragon

Arrogance King
Obliterated Onii Followers

Sloth King
Obliterated Troublesome Drunkards

Face-stuffing King
Obliterated Dessert-lovers

Rage King
Obliterated Blitzing Birds

Greed King
Obliterated Pervy Producer

Naughty King
Obliterated Casanova

Envy King
Obliterated Weirdo

Holler at Tomorrow!
Screamed at the Sea

Onii Hunter
Obliterated 100 Onii

Smooch Monster
Kissed a Princess 10 Times

Karefree Kingdom
Carefree Population Reached 100 People, Causing a Job Shortage

Tyrant King
Total Number of Incapacitated Citizens Reached 50

JUMP! Cannon King
Used JUMP! Cannon Over 50 Tries

Weapon King
Collected 15 Types of Weapons

Change up King
Acquired 20 Types of Outfits

Wig-out King
Acquired 20 Types of Masks

Helper King
Cleared 15 Quests

Humanitarian King
Cleared 30 Quests

Explorer King
Completed the Spot Encyclopaedia

Conquistador King
Completed the Monster Encyclopaedia

Gourmand King
Completed the Gourmet Encyclopaedia

Animal King
Completed the Animal Encyclopaedia

Music King
Completed the Humming Encyclopaedia

Gem King
Completed the Gem Encyclopaedia

Development King
Completed All Kingdom Plans

Fat Bucks King
Collected 100,000,000 Bol

SILVER

Together Forever
Lived happily ever after with that special someone

Bloooming Strength
Lived happily ever after with a flowery person

Sweet Future
Lived happily ever after with a cute person

Together Again
Lived happily ever after with a mysteriously reunited person

Sing a Song of Happiness
Lived happily ever after with a person who loves music

Unyielding Light
Lived happily ever after with a supple and beautiful person

Takin' Care of Love
Lived happily ever after with a pure and innocent person

Just As You Are
Lived happily ever after with a defiant person

Legend King
Completed the Record Encyclopaedia

GOLD

Hero King
Stopped Destruction of the World

Eternal Happiness
Everyone Lived Happily Ever After

PLATINUM

Kingiest King EVER
You fulfilled ALL accomplishments in the kingdom!

http://www.ps3trophies.org/game/new-little-kings-story/trophies/