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