Here is the full list of all 51 Mortal Kombat trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Complete Tutorial Mode
Perform a Fatality!
Perform a 10-hit combo with any fighter
Perform 1 "-ality" using the PlayStation®Vita system touchscreen
Spill 10000 pints of blood
Complete Fatality Trainer
Complete 25 Tower missions
Perform and land a Tag Combo
You've unlocked all Trophies!
Complete all 150 bonus tower missions
Gain Mastery of All Fighters
Complete Arcade Ladder on max difficulty without using a continue
Complete all Tower missions
Discover and fight Hidden Kombatant 1 in Arcade Ladder
Win 100 total Versus Matches
Unlock Mileena's 3rd Alternate Costume
Complete all Test Your Might mini-game challenges
Perform a Fatality with all playable fighters
Complete Arcade Ladder with All Fighters
Complete all Test Your Sight mini-game challenges
Complete 100 Versus Matches
Complete Story Mode 100%
Win 10 Ranked Online Matches in a row
Win A Ranked Online Match without jumping
Perform 8 throws in an Online Ranked Match
Win a Versus Match
Get a Flawless Victory in a Versus Match
Swipe your way through a set of all-new mini-game challenges
Discover and fight Hidden Kombatant 3 in Arcade Ladder
Gain Mastery of 1 Fighter
Discover and fight Hidden Kombatant 2 in Arcade Ladder
Unlock Kenshi, Skarlet, and Rain Alternate Costumes
Complete all Test Your Balance mini-game challenges
Complete 100 bonus tower missions
Discover and fight Hidden Kombatant 4 in Arcade Ladder
Unlock all Alternate Costumes
Complete Arcade Ladder without blocking (allowed to continue)
Perform every fighter's hidden finishing move
Perform every fighter's forward and backwards throws
Get all MK Dragons in Test Your Luck
Successfully land every playable fighter's X-Ray
Unlock 100% of the Krypt
Perform 1 of each type of "-ality"
Perform any fighter's hidden finishing move
Complete Story Mode 50%
Unlock 50% of the Krypt
Complete all Test Your Strike mini-game challenges
Discover all the deathtraps in Test Your Balance
Complete 50 bonus tower missions
Complete Arcade Ladder with Any Fighter
Win Arcade Tag Ladder with robot Sektor and Cyrax