There are 53 Trophies that can be collected.

Bronze

The Power Stone
Collected the Power Stone.

The Rhythm Stone
Collected the Rhythm Stone.

The Mind Stone
Collected the Mind Stone.

The Time Stone
Collected the Time Stone.

The Soul Stone
Collected the Soul Stone.

The Space Stone
Collected the Space Stone.

The Reality Stone
Collected the Reality Stone.

Squad Initiate
Completed Story Mode on Easy Difficulty.

Safety First
Defend the S.H.I.E.L.D. Building without losing a power node.

Elite Hack Master
Completed every Hack challenge.

Robo Racer
Completed every race challenge.

Stark Certified
Completed all of Iron Man's Heroic Feats.

Deadly Darling
Completed all of Black Widow's Heroic Feats.

Slice 'N Dice
Completed all of Wolverine's Heroic Feats.

T-Rex Nino
Completed all of Reptil's Heroic Feats.

The Hulkster
Completed all of Hulk's Heroic Feats.

Law and Order
Completed all of She Hulk's Heroic Feats.

The Human Rocket
Completed all of Nova's Heroic Feats.

Mighter then Thou!
Completed all of Thor's Heroic Feats.

Clearly Forceful
Completed all of Invisible Woman's Heroic Feats.

Woman with Vision
Completed all of Scarlet Witch's Heroic Feats.

Flying High
Completed all of Falcon's Heroic Feats.

Speed Thrills
Completed all of Quicksilver's Heroic Feats.

Webslinger
Completed all of Spider-man's Heroic Feats.

You've got the Super Power!
Collect all Power Stone Fragments.

You are feeling the Rhythm!
Collected all Rhythm Stone Fragments.

Time Management!
Collected all Time Stone Fragments.

Mind over Mind Fragments!
Collect all Mind Stone Fragments.

The Soul of a Hero!
Collected all Soul Stone Fragments.

Shiny Space Fragments!
Collected all Space Stone Fragments.

Reality Fragmented!
Collected all Reality Stone Fragments.

Heroic Attack!
Performed a Heroic attack.

Heroic Hero!
Defeat six or more enemies with a single heroic attack.

Deflected!
Reflected an enemies attack back at them.

Super Hero Up!
Revived a teammate.

Hero Punch
Broke through the defenses of a defending enemy.

Silver

Squad Member
Completed Story Mode on Normal Difficulty.

Challenge Master
Completed each challenge at least once.

Take that Villain!
Defeated an enemy with a parry.

Super Revive Hero
Revived a team mate 10 times.

Big Red
Complete all of Red Skull's Heroic Feats.

Cap!
Complete all of Captain America's Heroic Feats.

Not just a side kick
Complete all of Bucky's Heroic Feats.

Gold

Squad Hero
Completed Story Mode on Challenging Difficulty.

Super Achiever!
Completed all Heroic Feats!

Fragment Collector
Collected all Stone Fragments.

Platinum

Platinum
Earned all trophies.

6 Secret

http://www.ps3trophies.org/game/marvel-super-hero-squad-the-infinity-gauntlet/trophies/