Successfully complete one of the following tasks to get a trophy:

The Birth of an Assassin (Bronze): Be reborn as Ezio Auditore Da Firenze.
Arrivederci Abstergo (Bronze): Break out of Abstergo.
Myth Maker (Bronze): Find the 8 statuettes in Monteriggioni.
Vitruvian Man (Bronze): Unlock all 20 pieces of Subject 16's video.
Street Cleaner (Bronze): Hide 5 dead bodies in a Bale of Hay.
Fly Swatter (Bronze): Kick a Guard while using the Flying Machine.
Messer Sandman (Bronze): Stun 4 guards at once by throwing sand in their face.
Doctor (Bronze): Perform an Air Assassination on a Poisoned NPC.
No-hitter (Bronze): Kill 10 enemies while remaining in conflict without being hit.
Kleptomaniac (Bronze): Pickpocket 1000 Florins.
Lightning Strike (Bronze): Sprint for 100 meters.
Sweeper (Bronze): Sweep 5 guards at once by using a Long Weapon.
Venetian Gladiator (Bronze): Discover the Assassin's Tomb inside Santa Maria della Visitazione.
I can see your house from here! (Bronze): Discover the Assassin's Tomb inside Torre Grossa.
Hallowed be thy name (Bronze): Discover the Assassin's Tomb inside the Basilica di San Marco.
Prison Escape (Bronze): Discover the Assassin's Tomb inside the Rocca di Ravaldino fortress.
Choir Boy (Bronze): Discover the Assassin's Tomb inside Santa Maria del Flore (The Duomo).
Assassin for Hire (Bronze): Complete your first assassination mission for Lorenzo Il Magnifico.
Macho Man (Bronze): Defend a woman's honor.
Steal Home (Bronze): Win a race against thieves!
Show your Colors (Bronze): Wear the Auditore cape in each city.
Handy Man (Bronze): Upgrade a building in the Stronghold.
I like the view (Bronze): Synchronize 10 View Points.
High Dive (Bronze): Perform a Leap of Faith from the Top of Florence's Glotto's Campanile.
Mailman (Bronze): Intercept a Borgia Courrier.
Tip of the Iceberg (Bronze): Use your Eagle Vision to scan a Glyph in the environment.
A Piece of the Puzzle (Bronze): Unlock a piece of Subject 16's video.
Art Connoisseur (Bronze): Buy a Painting from Florence and Venice.
Podestà of Monteriggioni (Bronze): Reach 80% of the your stronghold's total value.
Perfect Harmony (Bronze): Tint your clothes with those colors: Wetland Ebony and Wetland Ivory.
In Memory of Petruccio (Bronze): Collect all the Feathers.
Red Light Addict (Bronze): Spend 5000 florins on Courtesans.
Man of the People (Bronze): Toss more than 300 florins on the ground.
Victory lies in preparation. (Bronze): Get all Hidden Blades, Item Pouches and Armor upgrades for Ezio.
Welcome to the Animus 2.0 (Silver): Enter the Animus 2.0.
The Pain of Betrayal (Silver): Complete DNA Sequence 1.
Vengeance (Silver): Complete DNA Sequence 2.
Exit the Son (Silver): Complete DNA Sequence 3.
Bloody Sunday (Silver): Complete DNA Sequence 4.
Undertaker (Silver): Discover the Assassin's Tomb inside the catacombs under Santa Maria Novella.
The Conspirators (Silver): Complete DNA Sequence 5.
An Unexpected Journey (Silver): Complete DNA Sequence 6.
Bleeding Effect (Silver): Complete training and reenter the Animus.
The Merchant of Venice (Silver): Complete DNA Sequence 7.
The Impenetrable Palazzo (Silver): Complete DNA Sequence 8.
Masquerade (Silver): Complete DNA Sequence 9.
Blanca's Man (Silver): Complete DNA Sequence 10.
The Prophet (Silver): Complete DNA Sequence 11.
The Vault (Silver): Complete DNA Seqeunce 14.
An Old Friend Returns (Gold): Escape the hideout.
Master Assassin (Platinum): Unlock all trophies.