Here is the full list of all 45 LittleBigPlanet Karting trophies - there are 34 bronze, 6 silver, 4 gold and 1 platinum.
Star a planet in Story mode
Complete the main path of Hoard, Sweet Hoard
Complete the main path of LittleBigPlanet™
Achieve a 5 hit streak in any Story battle level
Hit 50 Hoard minions in Story mode with any weapon
Accumulate a 5x score multiplier in a Story level
Dive into 25 community levels and complete those levels
Publish a level and have 10 different players complete the level
Complete all the tutorials on the first planet, LittleBigPlanet™
Defend against 30 attacks from opponents in any level
Place 1st in 25 different online levels with other human players
Complete 25 community levels
Beat a score posted by a friend on any community level
Complete a level a friend has written a review for
Drift non-stop for 10 seconds without stopping in any racing Story level
Chain three different grapples without touching the ground
Upload a photo taken from any level
Completely populate your profile page
Add a level to your queue
Complete a level in Team Picks
Complete a level with less than 5 playthroughs and leave a review
Play any level in your Recent Activity
Create a custom weapon in Create mode
Create a custom object inside one of your levels
Create a personalized planet
Create three cooperative levels and three versus levels
Slap an opponent on any level
Build and save any level created in Create mode
Create a custom pod
Change your ride
Change your costume
Earn all the LittleBigPlanet™ Karting trophies to unlock this platinum trophy
Complete the main path of Monster Islands
Complete the main path of Victoria's Laboratory
Complete the main path of The Progress Emporium
Complete the main path of Eve's Asylum
Complete the main path of The Space Bass
Spend 30 minutes in Create Mode
Watch all of the creation tutorials from start to finish
Host a playgroup with three other players in your Pod
Star every 'finale' level in the main story
Complete the main path of Story mode
Star every level in the Story mode
Spend 24 active hours in Create mode
Complete 100 community levels