Here is the full list of all 51 Assassin's Creed: Brotherhood trophies - there are 36 bronze, 13 silver, 1 gold and 1 platinum.
Win every trophy.
Receive 100% synch in ACB and full synch in all missions of the Da Vinci Disappearance.
Solve all of Subject 16’s puzzles.
Remove All Borgia Flags in Rome.
Win the highest bet at the Fights.
Complete the Da Vinci Disappearance.
Collect All Feathers.
Win 10000 florins playing Hazard.
Jump with the parachute off the top of Castel Sant'Angelo.
Perform an Execution Streak of 10 kills.
Replay a Memory.
Earn 3 gold medals in the Animus Virtual Training Program.
Discover the Shrine in Palazzo Laterano.
Discover the Shrine in Il Colosseo.
Double Assassinate from a parachute.
Discover the Shrine in the Basilica di San Pietro.
Destroy the Tank.
Destroy the Naval Cannon.
Destroy the Bomber.
Discover the Shrine in the Catacombe di Roma.
Discover the Shrine in the Cloaca Maxima.
Beat up the 5 thirsty harlequins.
Kill a guard with a broom.
Throw a Long Weapon, Heavy Weapon, and Smoke bomb more than 10 m at a guard.
Secure the Apple of Eden.
Complete DNA Sequence 9.
Complete DNA Sequence 8.
Complete DNA Sequence 7.
Achieve 100% Synchronization in any Sequence other than Sequence 1.
Complete 10 Guild Challenges.
Train a recruit up to the Rank of Assassin.
Steal 5 horses from their riders, while remaining on horseback.
Burn All Borgia Towers.
Kill 10 guards with a single arrow storm.
Complete DNA Sequence 6.
Complete DNA Sequence 5.
Complete DNA Sequence 4.
Destroy the Machine Gun.
Throw money in a well.
Recruit 3 Assassins.
Complete DNA Sequence 3.
Pay 500 florins to an orator, then pickpocket him afterward.
Renovate 5 buildings in the Antico district.
Kill a guard with the bag that drops from a lift.
Complete DNA Sequence 2.
Discover the Shrine in the Terme di Traiano.
Find 1 Artifact in 2012.
Access your email in 2012.
Find a secure place to hide and re-enter the Animus.
Complete DNA Sequence 1.
Attempt to access DNA Sequence 9 for the first time.