Here is the full list of all 13 Tumble trophies - there are 9 bronze, 3 silver and 1 gold.
Build a 2m tower within 35 seconds
Build a 1m tower
Earn 5 Gold Medals
Earn 50 Gold Medals
Earn at least one medal on every level
Score 3000 points on a Limpet Mine challenge
Fit 25 blocks on a platform in a Use Em All Challenge
Total Build Height of 5m
Total Build Height of 100m
Total Build Height of 500m
Play a Multiplayer Tournament
Build a 2m tower in Multiplayer Mode
Blow a block out of the arena in a Limpet Mine Challenge