There are 14 Trophies that can be collected.

Bronze

The Answer
Use 42 InstantRocks™ to finish a level

Jeff
Use 32 bridges to finish a level

Stackmate
Trap Toki Tori between two Switchbricks

Forest Falls
Complete all Forest Falls normal levels

Forest Falls Hard
Complete all Forest Falls hard levels

Creepy Castle
Complete all Creepy Castle normal levels

Creepy Castle Hard
Complete all Creepy Castle hard levels

Slimy Sewer
Complete all Slimy Sewer normal levels

Bubble Barrage
Complete all Bubble Barrage normal levels

Tunnel of Love
Find the Tunnel of Love

Dizzy
Make Toki Tori dizzy

Silver

True Champion
Complete all normal levels without using the Wildcard

Slimy Sewer Hard
Complete all Slimy Sewer hard levels

Gold

Bubble Barrage Hard
Complete all Bubble Barrage hard levels

http://www.ps3trophies.com/forums/ps3-trophy-news/6889-toki-tori-trophy-list.html