Here is the full list of all 31 The Legend of Korra trophies - there are 12 bronze, 14 silver, 4 gold and 1 platinum.
Completed a Naga Running sequence without hitting anything.
Completed Chapter 4.
Went into Clash Mode 10 times.
Dodged 100 times.
Got 10 knock-outs in Pro-bending matches.
Completed Chapter 3.
Used your first equipped item.
Jumped 100 times.
Entered the Collection Screen for the first time after finding a treasure.
Equipped your first item on the Korra's Room.
Bought your first item at the shop.
Completed Chapter 2.
Completed Chapter 1.
Got all other trophies.
Completed Chapter 5.
Completed Chapter 6.
Completed Chapter 7.
Completed Chapter 8.
Completed the game on Extreme difficulty.
Obtained all combos.
Maxed out all bending types.
Purchased 12 talismans.
Collected every treasure item.
Countered 100 times.
Performed 100 Finishing Moves.
Spirit-bended 200 dark spirits.
Went into Avatar State 10 times.
Won a Face-Off in a Pro-bending match.
Completed the highest difficulty of Pro-bending.
Completed all tutorials.
Collected 10 cabbages.