There are 12 Trophies that can be collected.

Bronze

Hello World
Clear Report 1 in Single Player Story Mode.

Apprentice Dancer
Achieve 25% in Single Player Ulala's Dance Mode.

Awesome Dancer
Achieve 50% in Single Player Ulala's Dance Mode.

Skilled Dancer
Achieve 100% in Single Player Ulala's Dance Mode.

HOOOOO!!!!
Rescue Space Michael.

Passionate Reporter
Rescue Jaguar.

Skilled Reporter
Earn a perfect rating in any one Report in Single Player Story Mode.

Silver

Fever Dancer
Clear the Single Player Ulala's Dance Mode.

Competent Reporter
Clear Reports 1-6 in Single Player Story Mode.

Excellent Reporter
Clear Reports 1-6 in Single Player Story Mode for the 2nd World (Extra Mode).

Secret Explorer
Clear all the hidden commands.

Gold

Perfect Reporter
Earn perfect ratings for all the Reports in Single Player Story Mode.

http://www.ps3trophies.com/forums/ps3-trophy-news/2846-space-channel-5-part-2-trophy-list.html