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.
Kill 10 guards with a single arrow storm.
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.
Win 10000 florins playing Hazard.
Discover the Shrine in the Basilica di San Pietro.
Double Assassinate from a parachute.
Jump with the parachute off the top of Castel Sant'Angelo.
Discover the Shrine in the Cloaca Maxima.
Win the highest bet at the Fights.
Collect All Feathers.
Destroy the Naval Cannon.
Discover the Shrine in Il Colosseo.
Steal 5 horses from their riders, while remaining on horseback.
Kill a guard with a broom.
Discover the Shrine in Palazzo Laterano.
Secure the Apple of Eden.
Complete DNA Sequence 9.
Complete DNA Sequence 8.
Kill a guard with the bag that drops from a lift.
Complete DNA Sequence 7.
Throw a Long Weapon, Heavy Weapon, and Smoke bomb more than 10 m at a guard.
Discover the Shrine in the Catacombe di Roma.
Burn All Borgia Towers.
Replay a Memory.
Throw money in a well.
Train a recruit up to the Rank of Assassin.
Destroy the Bomber.
Destroy the Tank.
Complete DNA Sequence 6.
Complete DNA Sequence 5.
Complete DNA Sequence 4.
Destroy the Machine Gun.
Recruit 3 Assassins.
Complete 10 Guild Challenges.
Complete DNA Sequence 3.
Pay 500 florins to an orator, then pickpocket him afterward.
Renovate 5 buildings in the Antico district.
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 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.