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.
Collected every treasure item.
Collected 10 cabbages.
Completed the highest difficulty of Pro-bending.
Purchased 12 talismans.
Won a Face-Off in a Pro-bending match.
Spirit-bended 200 dark spirits.
Went into Avatar State 10 times.
Completed the game on Extreme difficulty.
Got 10 knock-outs in Pro-bending matches.
Obtained all combos.
Maxed out all bending types.
Performed 100 Finishing Moves.
Completed Chapter 8.
Completed all tutorials.
Completed Chapter 7.
Completed Chapter 6.
Completed Chapter 5.
Went into Clash Mode 10 times.
Countered 100 times.
Dodged 100 times.
Completed Chapter 4.
Used your first equipped item.
Completed Chapter 3.
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 a Naga Running sequence without hitting anything.
Completed Chapter 1.