There are 13 Trophies that can be collected.

BRONZE

Metal Head
Upgrade a song at the Tapesmith

Weapon Master
Use every weapon once

Gleam On!
Dodge and get the Gleam 50 times

Mr. Perfect
Complete any level without taking damage

This Channel Sucks
Break all the Skullmageddon monitors in the Rocket Dojo

Pick a Winner!
Nail all enemies with the hair pick

Victory!
Defeat Skullmageddon!

SILVER

Misters Perfect
Complete any level in co-op without taking any damage… with friendly fire enabled!

Double Dragon
Finish every stage cooperatively on Double Dragon difficulty with friendly fire enabled!

Single Dragon
Finish every stage solo on Double Dragon difficulty!

GOLD

Max Fidelity
Max out every song to level 50!!

2 SECRET

BRONZE

FuzzFace!!
Befriend everyone's most favoritest helpful character!

A Foot Face?
Become the hidden idol!

http://www.ps3trophies.org/game/double-dragon-neon/trophies/