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