Here is the full list of all 50 LEGO Rock Band trophies - there are 37 bronze, 10 silver, 2 gold and 1 platinum.
Collect all bronze, silver and gold trophies
All four band members score 100% notes hit
Complete a song with four band members
Score 100% notes hit as a Drummer
Score 100% notes hit as a Bassist
Complete all gigs on the World Tour (except for the Rock Marathon Setlist and Endless Setlist)
Complete the Endless Setlist on the World Tour
Complete the Rock Marathon Setlist on the World Tour
Score a 100% rating as a Vocalist
Hire all Entourage members
Complete the Story
Complete the Stop the Rock, Rock Power Challenge
Play at every venue on the World Tour
Unlock the Teleporter on the World Tour
Complete the Rock-It Fuel Rock Power Challenge
Complete the Kings of Rock 'n' Troll Rock Power Challenge
Purchase the 8th vehicle on the World Tour
Get 1000 Stars
Complete the Rock the Boat Rock Power Challenge
Purchase the 7th vehicle on the World Tour
Complete the Securi-T-Rex Rock Power Challenge
Purchase the 6th vehicle on the World Tour
Spend 1,000,000 studs on rock den furniture
Spend 100,000 studs on rock den furniture
Purchase one item of rock den furniture
Spend 1,000,000 studs or more on instruments
Purchase an instrument
Spend 1,000,000 studs or more on items of clothing
Spend 100,000 studs or more on items of clothing
Purchase an item of clothing
Complete the Rock the Crop Rock Power Challenge
Purchase the 5th vehicle on the World Tour
Get 1,000,000 fans
Purchase the 4th vehicle on the World Tour
Complete the Rocktopus Rock Power Challenge
Achieve a 100% Stud Recovery during a performance
Get 100 Stars
Purchase the 3rd vehicle on the World Tour
Complete the Shock Band Rock Power Challenge
Purchase the 2nd vehicle on the World Tour
Hire an Entourage member
Hire a Band Manager
Complete the Wreck 'n' Roll Rock Power Challenge
Hire a Road Crew
Score 100% notes hit as a Guitarist
Get 100 fans
Gold Star any song
Complete your first gig on the World Tour
Score 100% on the Guitar Solo in "The Final Countdown" on Expert
100% a guitar solo on Expert