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