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