There are 13 Trophies that can be earned in this title.

Bronze

Lightning Fast
Build a 2m tower within 35 seconds

Getting Taller
Build a 1m tower

Gold Dust
Earn 5 Gold Medals

Construction Complete
Earn at least one medal on every level

Tucked in Tight
Fit 25 blocks on a platform in a Use Em All Challenge

Having a Giraffe
Total Build Height of 5m

Giant Red Wood
Total Build Height of 100m

Victory is Yours
Play a Multiplayer Tournament

Working Together
Build a 2m tower in Multiplayer Mode

Silver

All The Glitters
Earn 50 Gold Medals

Master Blaster
Score 3000 points on a Limpet Mine challenge

Out of the Park
Blow a brick out of the arena in a Limpet Mine Challenge

Gold

Reach for the Stars
Total Build Height of 500m

http://www.ps3trophies.org/game/tumble/trophies/