Here is the full list of all 29 Shiftlings trophies - there are 10 bronze, 12 silver, 6 gold and 1 platinum.
Finish Hyperactivia in under 24 minutes
Finish Hyperactivia
Finish Event Horizon in under 16 minutes
Complete Event Horizon Level 3 while swapping no more than 11 times
Complete Event Horizon Level 3 while jumping no more than 14 times
Collect 30 bottles of Black Hola Cola in a single world
Finish Event Horizon
Keep both characters suspended in air at the same time for 4 seconds
Complete a level with a random multiplayer partner
Wrap the Shiftlings' cable all the way around an object
Collect all bottles of Black Hola Cola in a single level
Invite a friend to a multiplayer match
Shift for the first time
Earn all Trophies
Complete all levels in Time Attack mode
Complete the game
Collect all 150 bottles of Black Hola Cola
Defeat the giant robot boss at the end of each world without dying
Get stuck at the objective in Level 9 on Hyperactivia
Meet your end in six different ways
Jump on Hammerbot's head and live to tell the tale
Complete Earth 2.0 level 10 while jumping no more than 5 times
Complete Earth 2.0 level 10 while swapping no more than 11 times
Finish Veraville in under 26 minutes
Finish Earth 2.0 in under 31 minutes
Finish Sherbert in under 34 minutes
Finish Veraville
Finish Earth 2.0
Finish Sherbert