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