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