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