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.
Remove All Borgia Flags in Rome.
Steal 5 horses from their riders, while remaining on horseback.
Kill a guard with a broom.
Jump with the parachute off the top of Castel Sant'Angelo.
Throw a Long Weapon, Heavy Weapon, and Smoke bomb more than 10 m at a guard.
Beat up the 5 thirsty harlequins.
Secure the Apple of Eden.
Complete DNA Sequence 9.
Complete DNA Sequence 8.
Discover the Shrine in the Basilica di San Pietro.
Solve all of Subject 16’s puzzles.
Complete DNA Sequence 7.
Discover the Shrine in the Cloaca Maxima.
Discover the Shrine in Palazzo Laterano.
Burn All Borgia Towers.
Win 10000 florins playing Hazard.
Complete DNA Sequence 6.
Collect All Feathers.
Kill 10 guards with a single arrow storm.
Complete 10 Guild Challenges.
Complete DNA Sequence 5.
Train a recruit up to the Rank of Assassin.
Double Assassinate from a parachute.
Complete DNA Sequence 4.
Destroy the Tank.
Destroy the Naval Cannon.
Destroy the Bomber.
Destroy the Machine Gun.
Recruit 3 Assassins.
Perform an Execution Streak of 10 kills.
Earn 3 gold medals in the Animus Virtual Training Program.
Complete DNA Sequence 3.
Win the highest bet at the Fights.
Pay 500 florins to an orator, then pickpocket him afterward.
Kill a guard with the bag that drops from a lift.
Complete the Da Vinci Disappearance.
Renovate 5 buildings in the Antico district.
Discover the Shrine in Il Colosseo.
Throw money in a well.
Discover the Shrine in the Catacombe di Roma.
Replay a Memory.
Complete DNA Sequence 2.
Achieve 100% Synchronization in any Sequence other than Sequence 1.
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.