There are 14 Trophies that can be earned in this title.

Bronze

Photographer
Save 30 or more still images to the Gallery.

Performer
Save 10 or more moving images to the HDD.

Artist
Play Creation Mode 50 or more times.

Expert
Use all tools in Creation Mode.

Conductor
Get a 100% rhythm bonus in Challenge Mode.

Painter
Get a 100% line bonus in Challenge Mode.

Professional
Open the Mirror Stage.

Challenger
Play Match Mode 100 or more times.

Paint Master
Get a score of 75% or higher in Paint Challenge.

Line Master
Get a score of 3.5m or higher in Line Challenge.

Rainbow Master
Complete stage 10 in Rainbow Challenge.

Silver

Champion
Complete all stages with platinum medals.

Legend
Complete all stages, including the mirror stages, with platinum medals.

Gold

Beat Sketcher
Move the cursor a total of 10,000 m.

http://www.ps3trophies.org/game/beat-sketcher/trophies/