Here is the full list of all 51 Mortal Kombat trophies - there are 34 bronze, 15 silver, 1 gold and 1 platinum.
Complete 25 Tower missions
Complete Fatality Trainer
Complete Tutorial Mode
Perform a Fatality!
Unlock Hidden Fighter "Quan Chi"
Complete Story Mode 100%
Unlock Hidden Fighter "Cyber Sub-Zero"
Spill 10000 pints of blood
Complete Story Mode 50%
Perform a 10-hit combo with any fighter
You've unlocked all Trophies!
Perform every fighter's forward and backwards throws
Complete Arcade Ladder with Any Fighter
Complete Arcade Ladder with All Fighters
Perform a Fatality with all playable fighters
Complete 200 Versus matches (online OR offline)
Complete Arcade Ladder on max difficulty without using a continue
Win A Ranked Online Match without jumping
Complete Arcade Ladder without blocking (allowed to continue)
Win an Online Match
Win Arcade Tag Ladder with robot Sektor and Cyrax
Win 10 Ranked Online Matches in a row
Complete 100 Online Matches
Win 100 total Online Matches
Get a Flawless Victory in an Online Match
Earn 1000 Respect Points via king of the hill Matches
Unlock 50% of the Krypt
Unlock 100% of the Krypt
Earn 2500 Respect Points via king of the hill Matches
Win 10 king of the hill Matches in a row
Perform 8 throws in an Online Ranked Match
Win both rounds with timer running out in an Online Ranked Match
Comeback with under 10% health in an Online Ranked Match
Successfully land every playable fighter's X-Ray
Get all MK Dragons in Test Your Luck
Unlock all Alternate Costumes
Unlock Mileena's 3rd Alternate Costume
Gain Mastery of 1 Fighter
Gain Mastery of All Fighters
Complete all Test Your Might mini-game challenges
Complete all Test Your Strike mini-game challenges
Complete all Test Your Sight mini-game challenges
Complete all Tower missions
Perform and land a Tag Combo
Perform 1 of each type of "-ality"
Perform any fighter's hidden finishing move
Perform every fighter's hidden finishing move
Discover and fight Hidden Kombatant 1 in Arcade Ladder
Discover and fight Hidden Kombatant 2 in Arcade Ladder
Discover and fight Hidden Kombatant 3 in Arcade Ladder
Discover and fight Hidden Kombatant 4 in Arcade Ladder