There are 42 Trophies that can be collected.

Bronze

Dozabot Scrapper    
Get this trophy when you destroy 5 Dozabots     

Dozabot Ranger    
Get this trophy when you destroy 100 dozabots!     

Dozabot Reaper    
Get this trophy when you destroy 500 dozabots!     

Dozabot Nemesis    
Get this trophy when you destroy 1000 dozabots!

Lake Waka – Cloudberry Catcher    
Collected all Cloudberry medals in Lake Waka     

Lake Waka – Speed of the Wind    
Collect all Time medals in Lake Waka     

Lake Waka – Egg Ranger    
Lake Waka – Egg Ranger     

Lake Waka – Dozabot Hunter    
Collect all the Dozabot medals in Lake Waka

Karibu Valley – Cloudberry Catcher    
Collected all Cloudberry medals in Karibu Valley     

Karibu Valley – Speed of the Wind    
Collect all Time medals in Karibu Valley     

Karibu Valley- Egg Ranger    
Karibu Valley- Egg Ranger     

Karibu Valley – Dozabot Hunter    
Collect all the Dozabot medals in Karibu Valley

Noko Woods – Cloudberry Catcher    
Collected all Cloudberry medals in Noko Woods     

Noko Woods – Speed of the Wind    
Collect all Time medals in Noko Woods     

Noko Woods – Egg Ranger    
Noko Woods – Egg Ranger     

Noko Woods – Dozabot Hunter    
Collect all the Dozabot medals in Noko Woods

Doza Fortress – Cloudberry Catcher    
Collected all Cloudberry medals in Doza Fortress     

Doza Fortress – Speed of the Wind    
Collect all Time medals in Doza Fortress     

Doza Fortress – Egg Ranger    
Doza Fortress – Egg Ranger    

Doza Fortress – Dozabot Hunter    
Collect all the Dozabot medals in Doza Fortress

Silver

Dozabot Devastator    
Get this trophy when you destroy 5000 dozabots!     

Completed Lake Waka    
Cleared all of the levels in Lake Waka

Completed Karibu Valley    
Cleared all of the levels in Karibu Valley

Completed Noko Woods    
Cleared all of the levels in Noko Woods

Completed Doza Fortress    
Cleared all of the levels in Doza Fortress

Gold

Lake Waka – 100%    
Completed all Lake Waka challenges

Karibu Valley – 100%    
Completed all Karibu Valley challenges

Noko Woods – 100%    
Completed all Noko Woods challenges

Doza Fortress – 100%    
Completed all Doza Fortress challenges

Platinum

100% Clear    
This is the platinum trophy and is unlocked automatically when all the trophies have been unlocked

12 Secret

http://www.ps3trophies.org/game/okabu/trophies/