There are 17 Trophies that can be collected.

BRONZE

Super Heroes Unite
Finish arcade mode with each hero (Marvel Super Heroes)

Villains Unite
Finish arcade mode with each villain (Marvel Super Heroes)

Capcom Unite
Finish arcade mode with each Capcom character (Marvel vs. Capcom)

Marvel Unite
Finish arcade mode with each Marvel character (Marvel vs. Capcom)

From the Shadows
Finish arcade mode with each Hidden character (Marvel vs. Capcom)

Another Notch
Complete the third tier of the challenge “Another Notch”

Big Finish
Complete the fourth tier of the challenge “Big Finish”

Going Streaking
Complete the third tier of the challenge “Going Streaking"

Powers Combined
Complete the third tier of the challenge “Powers Combined" (Marvel vs. Capcom)

Duo of Heroes
Complete the third tier of the challenge “Duo of Heroes" (Marvel vs. Capcom)

War of the Gems
Complete the third tier of the challenge “War of the Gems" (Marvel Super Heroes)

Not a Scratch
Complete the second tier of the challenge “Not a Scratch"

Grinder
Complete the third tier of the challenge “Grinder"

SILVER

Marvel Legend
Finish arcade mode without losing a round (Marvel Super Heroes)

Crossover Legend
Finish arcade mode without losing a round (Marvel vs. Capcom)

Around The Universe
Win a match with every normally selectable character (Marvel Super Heroes)

Around The Multiverse
Win a match with every character (Marvel vs. Capcom)

http://www.ps3trophies.org/game/marvel-vs-capcom-origins/trophies/